In Romans 14, the subject is not clean and unclean foods but eating meat versus vegetarianism (verse 2). Paul admonishes Christians not to pass judgment on others for eating meat or for eating only vegetables (verse 3).
The question that confronted Paul was not that God's people were suggesting that somehow unclean animals had now been made clean, but the belief of some that no meat—even meat that had been created to be eaten with thanksgiving—should be eaten at all. The apostle points out that it would be wrong for the vegetarians to eat meat if they had doubts about it, as it would defile their consciences (verse 23). He concludes, "For whatever is not of faith is sin."
Verse 14 is a proof text used by the world to conclude that all meat is now fine to eat: "I know and am convinced by the Lord Jesus that there is nothing unclean of itself; but to him who considers anything to be unclean, to him it is unclean." This is another verse that has been poorly translated to conform to preconceived notions.
The problem is with the word "unclean," which does not appear in the Greek text. To mean "unclean," Paul would have used akarthatos, but instead, the text reads koinos, which means "common," "ordinary," "defiled," or "profane (as opposed to holy or consecrated)." Peter uses both "common" and "unclean" to describe meats in Acts 10:14, so there is obviously a difference between the terms.
We know that the Bible defines "unclean" meat in Leviticus 11 and Deuteronomy 14, but when is meat considered "common"? The only circumstances in which clean meats are common or defiled are when a clean animal dies naturally or is torn by beasts (Leviticus 22:8) or when the blood has not been properly drained from the meat (Leviticus 17:13-14; 3:17). Such animal flesh was called common because it could be given to strangers or aliens in Old Testament times if they wished to eat it (Deuteronomy 14:21). Similarly, in Acts 15:20, 29, the apostles forbade the Gentiles to eat the meat of a strangled animal or meat that had not been drained of blood.
In the case of Romans 14:14, it is likely that "defiled" would be the best term, as the meat under discussion was probably that offered to idols then sold in the marketplace for public consumption. To paraphrase, then, the verse should read: ". . . there is nothing defiled of itself; but to him who considers anything to be defiled, to him it is defiled." The meat was not defiled in fact, just in the minds of various church members, whom Paul had earlier called "weak" (verse 2). These "weak in the faith" Christians believed that, because the meat had been offered to a pagan idol, it had become spiritually defiled.
Paul explains in I Corinthians 8:4-7 that the demon behind the idol is nothing, for "there is no other God but one" (verse 4). Thus, there is no "spiritual" taint to the meat.
However, there is not in everyone that knowledge; for some, with consciousness of the idol, until now eat it as a thing offered to an idol; and their conscience, being weak, is defiled. But food does not commend us to God; for neither if we eat are we the better, nor if we do not eat are we the worse. (verses 7-8)
So we see that in these verses that Paul is not in any manner doing away with God's laws concerning clean and unclean meat. The topic does not even come up! He is discussing meat defiled or profaned due to its association with a pagan idol.