You probably know this already, but Yahweh's prominence on the coinage and in the Pledge of Allegiance is a relatively recent phenomenon. It wasn't until 1908 that 'In God We Trust' was mandated on the coinage, and 'under God' wasn't inserted into the Pledge until 1954, as part of a wider anti-communist reaction. The supposed areligiosity of the Founders is often overstated by modern-day atheists with an axe to grind. However, while you'd be hard pressed to find a more pompous and puritanical Christian than the likes of John Adams, even he was strongly supportive of the separation of church and state: "Nothing is more dreaded than the national government meddling with religion."
As to the Founders, whether or not they were religious, the abuse of their legends has gotten old many times already. Many political factions (though the Tea Party are the worst culprits) have misinterpreted, misrepresented, and straight up lied (or worse, not actually known) about their history and beliefs, and used this confusion as a platform for their opinions. It's disgusting.
Except perhaps religion meddling with the national government?
The idea that someone can claim some benefit via allegiance to actual God in a political setting is pretty scary, IMHO.
Looking at it I noticed that I'm from one of the least religious countries in the world (Denmark).
I suspect it depends on who you hang out with :-)
"If the Danish prime minister started confessing her belief in a god she'd be laughed out of the room."
As an 18 year old American, active in American politics (I've done minor campaigning, father is a US History teacher), this is utterly strange. A politician that was not some denomination of Christianity would be, most likely, completely unable to win a Presidential election. And that's even if they were a religion the Christian majority feels close to, such as Jewish. If they were Muslim, or so help them atheist, they would stand no chance at the White House.
I recently had a friend of 6 years from the UK come and visit for two weeks, and we had a number of discussions on cultural differences. When he mentioned that the majority of people in the UK were not religious, I was dumbfounded. I (foolishly) thought it was everywhere as it is here. In my community at least, to openly question the existence of a God is a social faux pas. I have an interesting perspective having been on both sides of the coin, but in the end it scares me as much as it scares you. The concept of God abounds in our Pledge of Allegiance, in our graduation ceremonies, in our political speeches--it is almost universally accepted and above question.