That's twisting things a bit. God doesn't accept our sin, He accepts our apology for it. And the Bible is start to finish about offerings and acceptance of those offerings. How did you miss that? In the beginning sacrifices are offered as atonement and in the end prayers asking for forgiveness are offered, as in "Forgive us our sins..."
Why does God remove His favor from men like David until they seek atonement? He does so because that is the prerequisite by which His favor (forgiveness) is given.
This conversation is now circular.
While I wish you the very best, I must leave you with Proverbs 18:2
Blessings to you