They were very firm believers in God, his word, and his principles.
Man's use and abuse of organized religion is what made them a bit wary of it and that is reflected in our constitution. They disagreed with the Catholic and or Protestant jihads that occurred in early Europe. European leaders mass murdered those who did follow the faith of the day. They frowned on tyranny.
All of our founding fathers believed in religious tolerance as long as that religion was free enough to believe that God gave us our rights. Why do you see that as a problem?
I agree with everything you just wrote. And I don't see religion as a problem. I am a Deist.