An Honest Question to Christian Readers

The week before Christmas, I was outside of a grocery store that had a sale on holiday hams. It struck me as odd that the birth of someone who was Jewish would be regularly celebrated by His followers with something that was not kosher, clearly forbidden in Leviticus 11. This would be no problem at all if the the entire Old Testament was rejected, but the creation story in Genesis and the Ten Commandments seem to be still taken seriously.

So, the question I've never understood is what criterion is used to determine what parts of the first five books is still operative and which parts God changed his mind about? In determining Christian theology, how do you know when it is o.k. to refer to the earlier sections and when are they obsolete? Is it opt-in or opt-out, that is, does there have to be reference to the passage in the New Testament for it still to be enforceable Divine command or does there have to be contradiction of it in the Gospels for it to be overturned? Or is the condition something else altogether? Growing up Jewish and watching Christians eat anything they wanted during Passover -- especially when it overlapped with Easter -- always left me curious about this.