Short answer: There is no reason why we should.
On the other hand, the "laws" that are being proposed are perfectly suited to barnyard animals....
Lost in all this is the nature of man qua man.
We should obey “higher” laws (as you call them) because some of them will make our society safer, more civil, more comfortable, more conducive to human happiness and survival. But not all laws based on the desires of God (as revealed to certain politically ambitious historical figures) are as conducive. I’m pretty happy we don’t stone people anymore for having sex outside of marriage.
BB: Short answer: There is no reason why we should.
And yet there is something inside us that causes us to know we are not supposed to live like that.