Actually, the claim by the Jehovah's Witnesses that the prohibitions of kashrut (Jewish Law regarding kosher food) were changed is not supported by Scripture.
The JW misunderstanding your are referring to has to do with their interpretation of Mark 7:19 where, in a discussion about the ritual washing of hands as practiced by the Pharisees, Jesus "declares all foods clean." Thus, say Jehovah's Witnesses (and some other Christians as well), Jesus lifted the kosher prohibitions demanded of people by the Mosaic Law.
There are several outstanding problems with this claim. The first is that kashrut (Mosaic kosher laws) applied only to Jews. So it cannot be said that Jesus freed humanity in general from observing food laws that were never demanded of them.
And if Mark 7:19 is where Jesus ends the prohibitions of kashrut, somebody forgot to tell Peter--and reportedly he is the one who told Mark what to include in his gospel!
You see, for even some time after Jesus' death and resurrection, and even some time after Pentecost, Peter, a Jewish Christian, is still eating kosher. We know this from three Biblical accounts. The first is in Acts 10, where Peter is given a vision of all types of animals forbidden to be eaten by kashrut. When instructed in the vision to slaughter the animals and eat them, Peter replies: "Certainly not, sir. For never have I eaten anything profane and unclean." (Acts 10:9-14) By the calculations of some, several years have passed since the Resurrection. Yet still, years after the events of Mark 7:19 (which traditionally Peter narrated to Mark), Saint Peter himself is still eating kosher.
The second is Galatians 2:11-14. Written by the apostle Paul circa 55 CE, Paul talks about an incident in which he argues about how Peter acted when around Gentiles regarding eating. Around 20 years have passed since the death and resurrection of Jesus, and Peter is still described as eating kosher!
What is often not discussed about Galatians is that though Paul mentions telling Peter to his face about how wrong he thinks Peter is, the abrupt way the story ends without telling what happens seems to imply that Paul didn't win the debate. Paul is describing an event that occurred in the past, before he wrote the letter to the Galatians. Paul's view was obviously changed by apostolic decree from what we read at Acts 21:15-26.
According to some calculations this visit of Paul to Jeruslaem likely happened as a result of the face-off described in Galatians (though some date the argument as happening later, but still shortly before Galatians was written, circa 49 CE). As Acts 21:20-21 demonstrates, Jewish Christians as a whole still saw themselves as under the Mosaic Law and lived their lives as Torah observant.
Years would pass after these events, and Paul would soften his view in Galatians for by 58 CE Paul would write in his letter to the Romans that Gentile Christians should not condemn Jewish Christians due to what food they ate or avoided. (Romans 14:1-23) The Gospel of Mark would be written shortly after these statements of Paul.
Thus the first century Christians never understood any of Jesus' words uttered by him as proclaiming an end to kashrut laws. Jewish Christians still ate kosher, and while Paul taught Gentile Christians that the kosher prohibitions did not apply to them, the Church as a whole still favored kashrut observance by Jewish Christians.
So what did Jesus' words in Mark mean? Obviously if Jesus had declared that kosher regulations had been lifted then none of the incidents reported in Acts or Galatians or the allowances in Romans would have happened and been written about.
Also, Jesus would likely have been stoned for saying something like that. Obviously people are reading something into Mark that Jesus never meant, especially in light of Jesus' words at Matthew 5:17-19.
Mark 7 describes a discussion about "ritual" hand washing as practiced by the Pharisees. The first few verses explain that they were not advocating hygienic behavior but ritual and moral cleanliness. We understand this because Jesus, in verses 21-23, states that people are made "unclean" by evil thoughts and evil actions. The Pharisees were claiming that eating food without undergoing a series of ritual baptisms beforehand made one just as impure.
Were the Pharisees going to marketplaces run by Gentiles and getting their food from pagans and heathens who themselves ritually sacrificed their animals beforehand to their pagan gods? Or course not! Was the food under discussion by the Pharisees kosher or not kosher? No Jew would be eating food that wasn't kosher, as Peter had exc!aimed in his conversation with Heaven. So the foods the Pharisees were claiming were unclean were kosher foods.
Thus Mark's statement that Jesus "declared all foods clean" meant that Jesus declared all kosher foods as ritually pure enough as they were, regardless if one ate them with washed or unwashed hands. Only much later would people, like the Jehovah's Witnesses read Mark's statements differently.
So the prohibitions you mentioned regarding pork and other non-kosher foods were never lifted.