Wow, what an interesting post! Clearly there is no simple, bright line rule for christians. Then again, Jesus commanded his disciples to spread the Gospel. Does the Gospel include the law? Are we imposing the Hebraic law and covenants upon the whole world? Or spreading salvation through Jesus? I think the latter, though with regard the law see the following verses:
1 Corinthians 9:20-22King James Version (KJV)
20 And unto the Jews I became as a Jew, that I might gain the Jews; to them that are under the law, as under the law, that I might gain them that are under the law;
21 To them that are without law, as without law, (being not without law to God, but under the law to Christ,) that I might gain them that are without law.
22 To the weak became I as weak, that I might gain the weak: I am made all things to all men, that I might by all means save some.
King James Version (KJV)
Public Domain
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So, my reading leads me to conclude that if you are one like Peter, and wrought effectually to the apostleship of the circumcision (see Galatians 2:8), then you ought to become as a Jew, as under the law, that you might gain them that are under the law. That means, observe Sabbath, do not go around eating ham sandiches and talking about how delicious that might be. How could you win people if you just go around breaking their traditions and culture?
By the same token, maybe you are one like Paul and work effectually among the Gentiles. In Japan, they eat alot of shellfish, unclean animals (shrimp tempura? tonkatsu?). If you follow Paul's example, you would become as without law, but under the law of Christ (1 Cor. 9:21), that you might gain them that are without law. It could render your Gospel less effective if you go around insulting your hosts by appearing to disrespect their fine cuisine, and always insisting on special dietary restrictions and strange eating habits. Who wants to take on Christ + all those useless foreign ideas? To a Gentile nation that has never heard of Abraham or Moses, it might seem like you are promoting some superstition or new fad diet, and separates you by making you seem not like them.