For it to be struck down someone would have to sue and the matter taken through the judiciary to the Supreme Court. For the first 150 or so years there was a bias towards Christianity and such laws didn't attract much opposition, if any. Things have changed.
Hmmm...I doubt that. I am a Catholic, and I know for one the Catholic religion wasn't even legal in most of the colonies until the late 1700s. I'd have to do research, but I'm sure some of these laws targeted Catholics as well as Quakers, Unitarians, and other non-mainstream Protestant groups.
There have to be some legal opinions on this from the time period.