So I take it,
“You shall have no other gods besides me” is something you don’t have to follow because it was a command given to Abraham?
I take it you meant Moses, not Abraham. But, the question is still a good one. This quote originates in the Decalogue, the so-called ten commandments given to Israel as a precursor to the entire Mosaic Law. I trust that you have read Jesus' commentary on these requirement as He developed their full weight (Matt. 5 - 8). The entire purpose of the Law was to drive Israel to its knees to say, "Now I see, I do not, cannot, will not obey. If you do not reach inside and save us, we have no hope." But, Israel began to formulate ways to believe they were actually obeying these things.
Notice, Jesus amplifies the "Thou shalt not commit adultery" to the point where even a glance at a woman is the equivalent of sinning. And, "If your right eye causes you to stumble..." well, you know the rest. He is driving Israel to cry, "Then what can we do?" Read the rich young ruler's episode. Even the disciples say, "Well then who can be saved?" Jesus' answer, "With man it is impossible, but with God it is possible." Catch the direction of the argument? The Law corners us until we say, "Help, I am evil and only you are holy." Even that cry is managed by God in those whom He is rescuing.
You probably don't actually attemtpt to do most of the so-called "commands" you have read in the Scriptures. You are not building an ark (I knew that), you are not marching around Jericho, you are not going home from Babylon, you are not naming the animals, you are not coming down from a tree. You intuitively know something/someone else is involved. That comes from hermeneutics. I am just saying pay attention to the audience.
But, yes, the devotion to the God of Israel, alone, is set out for us non-Jewish believers in the NT letters written specifically to us. Thus, I am not obeying the Exodus passage, or the Deut. passage, but I am obeyeing the same thing from my own (and your own) mail.