Obliged is a problem. We should strive to follow the law of God. We are not obliged because we cannot. That is what the New Covenant is all about -- not a free pass.
There are some notable exceptions:
Gentiles are not subject to the Law intended for Jews -- as decided at the Jerusalem Council, which reverted back to the Noahic Covenant as the basis for right and proper actions for those not of a Jewish persuasion.
We are not legalists, but under grace. By Paul's argument, that does not mean that we set aside the Law, but rather that we rightly understand that even if we wished we could never fulfill it. Christ did fulfill it and we are imputed His righteousness, so before God it is as if we had fulfilled the Law in its entirety.
There are some other new practices instituted by church under the New Covenant, i.e., WE are now the temple, so any legal activities surrounding temple issues (sacrifice, etc.) are annulled. The Sabbath is not in force as it was in pre-NC times. Rather, we celebrate the Lord's Day, and that not exactly in a Sabbatarian form. We are atoned for, so some of the Law surrounding atonement (different from sacrifice) are also annulled. And, noteably, God issued a new standard for food practices to Peter, and with those food practices also alternative standards of what makes one clean or unclean. In essence, one cannot be unclean if one is indwelt with the Holy Spirit.
There are other issues that I either don't have the time or the resources to develop here, but it is safe to say that the entire issue is MUCH MORE than a couple of phrases or a "do we or do we not" sort of exercise.