The funny thing is that the bible itself indicates that a Christian can eat meat that was sacrificed to idols provided he did it innocently as a regular meal and not as a religious rite, and was not stumbling anyone. Paul told the Corinthians that they can eat meat given them without inquiring of its origins. This shows that the pagan origin of the meat doesn't really matter to God. What matters is the intent with which it's eaten by the Christian and whether eating it in the presence of others with weaker consciences could stumble them. See 1 Corinthians 10:25-30
In contrast, JWs adopt an overly scrupulous pharisaic attitude of feeling compelled to research the origin of obscure practices to make sure there're no pagan roots hidden somewhere in its history. They are missing the point completely. According to 1 Corinthians 10:25-30 God does not stigmatize an otherwise innocent practice engaged in with innocence simply because of past association with paganism.