You are probably on the right track.
One side likes to believe in absolute moral standards which they themselves never live up to, advocating grace and forgiveness....
The other side emphasizes behavior and personal responsibility which they try mightily to live up to and expect their friends and family to do likewise.
Its like how you get disgusted when I listen to a preacher and apply peer pressure to get me to listen to N.P.R.
In contrast, I could care less what you do in the privacy of your own life...I figure you made the choice and its none of my business.
BTW....I don't insist that your kids believe in God, either....I just don't want it to be taught that God is a myth.