From what I have read in a number of Bible commentaries, including the Anchor Bible, the dietary restrictions listed in Acts 15:20 has to do with table fellowship among Jewish and Gentile Christians. Gentile Christians, while being free of Old Testament dietary laws, were to abstain from certain dietary practices for the sake of the Jewish Christians.
The Expositor's Bible Commentary, Volume 9, page 448 says: "These prohibitions have often been viewed as a compromise between two warring parties, which nullified the effect of James's earlier words and made the decision of the Jerusalem Council unacceptable to Paul. But in reality they should be viewed not as dealing with the principial issue of the council but as meeting certain practical concerns; not as being primarily theological but more sociological in nature; not as divine ordinances for acceptance before God but as concessions to the scruples of others for the sake of harmony within the church and the continuance of the Jewish Christian mission."
The Watchtower as usual takes Acts 15:20 out of context.