Yes, I would guess so, like everything else, choose the ones you want to do or not. I have to read on, but this one in particular was given to us by God, for He said, I am the Lord, your God. He doesn't explain why, except to say what not to do, because He doesn't have to, He is our Father.
I the time that this law was written (and I'm not sure how long thereafter), tattoos and making cuts into the flesh were parts of ritualistic worship to false gods, hence, He says, "I am the Lord, your God." He was forbidding them from worshiping other gods. It was not necessarily the what but the why. Tattoos do not have the same meaning any longer. Some of the kosher food laws had similar reasons and were lifted because they were no longer relevant by the time of Christ. It is the same type of prohibition as cremation. Cremation was not, to the best of my knowledge forbidden in Scripture, but it was forbidden for a time by the Church. The reason was that people were doing it as a protest against the belief in the resurrection of the body. Now that this is no longer an issue, the Church no longer has a problem with cremation. Likewise, married priests. This has not always been the rule and could possibly change in the future, but for now, it serves a relevant purpose. I'm sure there are more, but these are what I can think of off the top of my head.