Why should the US be "one nation under god", when the founding fathers were in fact not really religious and strongly emphasized the separation of church and state?

“Lighthouses are more useful than churches”
Benjamin Franklin

“This would be the best of all worlds, if there were no religion in it!”
John Adams

“Christianity is the most perverted system that ever shone on man”
Thomas Jefferson

Jefferson even wrote his own bible, without all the miracle humbug.
You can tell, I just watched “Religulous” :)

But seriously, how was it, that despite the fact that everything is constitution this, constitution that the church was able to “infiltrate” the state to this extent?