This is one I think about frequently. It would seem that this applies to JWs only if you are a JW (which I am, so this scripture bothers me a bit... sorry, can't shake it.)
However:
"in the final part of the days"
What days? Most OT authors looked toward the Messiah as their "last days". Does this mean when Jesus was on earth?
"the mountain of the house of Jehovah will become firmly established above the top of the mountains"
When did this occur? In 1914? Or more likely when Jesus said at John 2:19? "In answer Jesus said to them: “Break down this temple, and in three days I will raise it up."
"and to it all the nations must stream"
The natural Israelites had a chance to be a kingdom of priests. (Ex 19:6) But, they blew it. So, Jesus said at Matt 22:37,38: "“Jerusalem, Jerusalem, the killer of the prophets and stoner of those sent forth to her,—how often I wanted to gather your children together, the way a hen gathers her chicks together under her wings! But YOU people did not want it. ?Look! YOUR house is abandoned to YOU."
So, Paul was made an apostle to the nations. (Rom 11:13). The Gentiles were being invited in, thus "all nations".
And many peoples will certainly go and say: “Come, YOU people, and let us go up to the mountain of Jehovah, to the house of the God of Jacob; and he will instruct us about his ways, and we will walk in his paths.”
Many people preach. Not just JWs. Don't believe me? Just read sermons online. They're full of preaching, just like JWs. Many of them use God's name. Who is to say that only JWs do this?
For out of Zion law will go forth, and the word of Jehovah out of Jerusalem. 4 And he will certainly render judgment among the nations and set matters straight respecting many peoples. And they will have to beat their swords into plowshares and their spears into pruning shears. Nation will not lift up sword against nation, neither will they learn war anymore.
You got me. Since judgment hasn't been rendered, yet, I would venture to say that this has not been fulfilled. Once judgment has been rendered and matters are set straight, then we will see the latter part in it's entirety, where entire nations will not war against other nations, not just JWs in one country not warring against JWs in another country.
Just my opinion on this. Read the commentaries at bible.cc on these verses. It's kinda all over the board. Who is right? Who isn't? Who's to say?