In answering this question you have to understand something about the origins of the Israelite people. Archaeologist working in the Levant are fairly confident that Biblical descriptions of the Exodus and the large scale conquest under Joshua as a whole are literary inventions and that Israel emerged as a distinct people at the end of the Late Bronze Age largely from the already present, indigenous Canaanite population with some input from nomadic peoples (for good discussions on what archaeologists in the field know and why, see American archaeologist William Dever's Who Were the Early Israelites and Where Did They Come From? (2003) as well as Israeli archaeologists Israel Finkelstein and Amihai Mazar's The Quest for the Historical Israel: Debating Archaeology and the History of Early Israel (2007)). This was a time when Egyptian hegemony of the area waned which allowed for the gradual formation of independent nation states such as Moab, Edom, Phoenicia, etc. as well as Israel. Thus, at the end of the 13th century the first undisputed reference to the "people," not nation, is found in the Mernephtah Stele (the difference between an urbanized state and a people is given in the hieroglyphs). Once this is understood, Israelite religion as a whole is to be studied as a subset of the larger Canaanite religion.
As can be gleaned from material from Ugarit (c. 1400 BCE) as well as other archaeological finds, Canaanite religion was characterized by the belief in the high god El and his consort Asherah who are presented as deities of theogonic times. El is repeatedly pictured as the wise old patriarchal father who along with his consort created the world. The material from Ugarit also ascribes to El the designation "Bull El" so that the Bull served as a symbol for him. Included in the world which El created are the so called "sons of El" (Ug. bani 'Ili-mi) who are cosmogonic deities that largely embody forces and phenomena of the natural world. The material from Ugarit also specifies that there are 70 "sons of El" and that most important of these is the storm God Baal whose battles with the other sons for control of the divine council under El is recounted in the so called "Baal Cycle." There are other features of note, particularly the divine messengers (i.e. malakim), but what has been said should be enough to get a good grasp of the basics of Canaanite religion.
Turning to Israelite religion, one should first observe that the very name "IsraEL" already assumes the importance of the God El in the Israelite tradition as do the names El Shadday, El Elyon, El Olam seen throughout Genesis. Secondly, descriptions of God in the Bible likewise cast him as the patriarchal father who stands at the head of a divine council comprised of the "sons of El" (Heb. bene 'elim) (cf. Psa 29:1, 89:7) elsewhere also called the "sons of Elohim" (Heb. bene 'elohim) (cf. Gen 6:4, etc.). Even Biblical episodes which show supposedly "apostate" practices, such as the admittedly literary episode of Aaron and the golden calf as well as the likely historical setting up of golden calves at Bethel and Dan by Rehoboam (1Ki 12:28, 29), also point to ways of venerating El, though this particular form was evidently not acceptable to these Biblical writers. One should note, however, that Bull imagery is used even by the writer of Numbers (cf. Num 24:8). What we see then is that the same depiction of El from Canaanite religion is accepted throughout Israelite religion, both "Biblical" and non-biblical.
Returning to the "sons of El," the Biblical writers conceive of these as lower divinities and not, as later Jewish and Christian thinkers do, as "angels." Deuteronomy 32:8, 9 describes how Elyon (i.e. El, cf. Gen 14:18, 19, 20, etc.) divided up the nations "after the number of the sons of El" (for the original reading "El" over the reading "Israel" in the Masoretic Text, see Sidnie White Crawford, et. al. "Sample Editions of the Oxford Hebrew Bible: Deuteronomy 32:1-9, 1 Kings 11:1-8, and Jeremiah 27:1-10 (34 G)" Vetus Testamentum 58 (2008): 353-57; cf. Septuagint)). When it is remembered that the material from Ugarit gives the number of the "sons of El" as 70, it is no wonder that one finds the same number of nations given in the so called "table of nations" (cf. Gen 10-11). The passage from Deuteronomy is interesting since it speaks of Yahweh, who I will get to in a bit, as having Israel as his "allotment" (Heb. HLQ). The use of this word throughout Deuteronomy is equally interesting. Thus one reads at Deuteronomy 4:18, 19:
"And beware lest you lift up your eyes to heaven, and when you see the sun and the moon and the stars, all the host of heaven, you be drawn away and worship them and serve them, things which Yahweh your God has allotted (Heb. HLQ) to all the peoples under the whole heaven. But Yahweh has taken you, and brought you forth out of the iron furnace, out of Egypt, to be a people of his own possession, as at this day."
This passage continues the same idea so that while Yahweh's "allotment" is Israel, the other nations worship "sons of El" who are represented in this passage by celestial phenomena. Again, Deuteronomy 29:21-28 speaks of a future generation of Israelites whose land would be destroyed by Yahweh because they "went and served other gods (Heb. elohim) and worshiped them, gods (Heb. elohim) whom they had not known and whom he had not allotted (Heb. HLQ) to them" (Deu 29:26). Here is the final piece of the puzzle where the biblical writer acknowledges that these "sons of El" who El allotted to the other nations to worship are in fact deities that the people of Israel should not worship as they are Yahweh's "allotment." Thus the writer of Deuteronomy assumes what was seen in Canaanite religion where the "sons of El" are lower deities of the divine council under the high god El. Deuteronomy is not the only writer to make this assumption. Thus the author of Psalm 89 speaks of the "sons of El" as part of the "council of the holy ones" who are inferior to Yahweh, the author of Psalm 82 presents God as presiding over the "council of El" and passing judgment on the "sons of Elyon" for failing to act justly so that God himself takes control of all the nations, the author of Job presents the "son of Elohim" appearing before Yahweh in what is also clearly a council setting. Though the Biblical writers are against their worship, they also show that other did in fact do so which makes sense considering their Canaanite background (2Ki 17:16; 21:3, 23:4, etc.).
It was mentioned earlier that the most important of the "sons of El" in Canaanite religion was Baal. In keeping with the Biblical writers' position which does not express any deep interest in the "sons of El" due to their singular focus on El or Yahweh (cf. Exo 23:13), the person of Baal is only mentioned in contexts which speak of the so called "apostate" worship of Israelites. Even so, the Biblical writers utilize Canaanite traditions about Baal for their own depictions of Yahweh. For example, the Baal Cycle from Ugarit relates how Mot, the god of death, threatens Baal by saying that he will defeat him as "when [Baal] struck down Litan (ltn), the fleeing serpent (btn brh), annihilated the twisting serpent (btn 'qltn), the powerful one with seven heads" (KTU 1.5:I.1-3). This same story is utilized by Isaiah who similarly speaks of a time when Yahweh "will punish Leviathan (lwytn) the fleeing serpent (nhs brh), Leviathan the twisting serpent (nhs 'qltn)" (Isaiah 27:1).This story is also utilized at Psalm 74:14 where the psalmist, unlike Isaiah who places it in the future, speaks of Yahweh as having "crushed the heads (note the plural) of Leviathan" sometime in the past. Further, in the same way that Baal is given the epithet of "the Rider of Clouds" at Ugarit, the Bible depicts Yahweh as riding a cloud chariot through the heavens (Deu 33:26; Psa 68:34 , 104:3; Isa 19:1). While much more could be said on this, what we see in the Biblical writers is an attack on Baal worship on the one hand while on the other their ascription of Baal's character, exploits, and imagery to the figure of Yahweh. The backdrop for all this is what is imagined in 1 Kings 18 where an older, Canaanite form of Israelite worship which elevated Baal was being practiced by the people in general and a newer Yahweh cult seeks to make converts to it so that it must compete with it. This explains why the Biblical writers seek to identify Yahweh with both Canaanite El and Baal so as to make him more attractive for worship (cf. Exo 6:2, 3). The Biblical writers, however, have flipped this around to make their Yahweh cult as the original form of Israelite worship and the "apostates" worship as due to foreign influence. This of course is the same kind of historical revision that many throughout the centuries have done when supplanting a previous way of doing things. Thus your question should not be "why were the Israelites so easily influenced by foreign Gods?" but rather "why did the worship of Yahweh emerge among the people of Israel and try to assert itself upon the indigenous way of worship?"
This question is much harder to answer because unlike El, Ashurah, Baal, etc. the deity of Yahweh is unknown among the Canaanites nor is there any indisputable find which locates his origins elsewhere. One clue is offered by the Biblical writers who point to Yahweh's originating from the northwestern Arabian peninsula as is indicated by his association with Sinai (Deu 33:2), Seir (Jud 5:4, 5), Edom (Psa 68:7, 8), Paran (Hab 3:3), and Teman (Hab 3:3). if so, then it would seem that Yahweh worship is in fact the "foreign" element. I cannot say more on the origins of Yahweh worship because, to be frank, I have not researched all the views on this thoroughly enough to form an opinion.
What I do know is that veneration of Yahweh must have been part of the state cult by the middle of the 9th century BCE as may be seen from the reference to Yahweh in the Mesha Stele. Undisputed onomastic evidence, i.e. evidence from personal names, likewise begins from the 9th century BCE. These dates are earlier than the reigns of Hezekiah (late 8th century BCE) and Josiah (mid-late 7th century BCE) who are hailed as the big Yahwist reformers. However, at the end of the 9th century the Bible states that Jehu destroyed the temple of Baal yet interesting left the golden calves setup by Rehoboam at Bethel and Dan (2Ki 10:23-30). This makes sense since it is to be remembered that the Bull was originally associated with El who was later equated with Yahweh. Later Biblical writers of course see this as an unacceptable form to worship Yahweh due to their aniconism which was obviously not shared by those in an earlier period. In the 8th century Hezekiah went even further and removed the Asherah, that is, the pillars which symbolized El's consort Asherah (2Ki 18:4). Here archaeology shows what was actually occurring was not Israelites gone "apostate" for Canaanite deities which Hezekiah was attacking, but rather Israelites who were holding to remnants of older Canaanite worship which had now equated Yahweh with El. Thus two ostrica from Kuntillet 'Ajrud as well as a third from Khirbet el-Qom all dating to the 8th century BCE speak of "Yahweh of Samaria and his Asherah," "Yahweh of Teman and his Asherah," and "Yahweh [and] ... his Asherah" thus showing a clear association between Asherah and Yahweh which is made on the basis that the Canaanite El of the old Canaanite religion had now been identified with Yahweh. What Hezekiah was attacking then was a form of Yahweh worship which he considered to be improper. Others did not share his view, however, since the Asherah went up again after his reign only to be torn down yet again by Josiah. The Bible's description of this is interesting since it shows conclusively that they were features of the Temple itself: "[Josiah] brought out the Asherah from the house of Yahweh, outside Jerusalem, to the brook Kidron, and burned it at the brook Kidron" (2 Kings 23:6). This also supports what was said above that the use of the Asherah were part of Yahweh worship and not some "foreign" God.
More could be discussed on this, but I will leave it here since I have spent to much time typing this up already. Basically, what is seen from an examination of both the Jewish Scriptures and the archaeological data is the origins of the Israelite people from an indigenous Canaanite population whose religion was Canaanite as well, but at some point between the 13th century and the mid-9th century BCE incorporated the deity Yahweh into their religious tradition to become its own distinctive tradition. This incorporation brought about a modification of the old Canaanite religious tradition which was carried out by people in diverse ways. The common people seemed to be happy with merely equating Yahweh with El and continuing on as usual. Others saw that Yahweh should be greater emphasized and so brought about more radical modifications to the old religion which many were not happy to follow. It is due to this that Yahweh worship as it later came to be took a long time to take hold and the winners of the debate, i.e. the Biblical writers, represented that struggle as one of religious truth, from their standpoint anyways, struggling against a wayward, obstinate population. The real situation, however, was as the people replied to Jeremiah even in the late 7th-early 6th century BCE: "But we will do everything that we have vowed, burn incense to the queen of heaven and pour out libations to her, as we did, both we and our fathers, our kings and our princes, in the cities of Judah and in the streets of Jerusalem" (Jer 44:17; here the "queen of heaven" is probably a later development of the Asherah tradition). Thus the people were not "easily influenced" by foreign gods but rather worshipped Yahweh as they had for hundreds of years against the "extremist" forms of Yahweh worship pushed at various times by a few kings and people who claimed to be prophets.