So the fact is, separation of church and state evolved in the US — it was not part of US foundings.
jar and Taz already made this point, but I feel that it is important enough to repeat. But first, I'd like to point out that reading the "intent" of people who died 200 years ago is a bit problematic. The reason is that there were many people involved in the founding of the Republic, and there were many people involved in framing the Constitution. Like most political documents, the Constitution isn't based on some simple, timeless principles; it is a set of compromises between political factions that had competing visions of what the Republic should be like. The framers had lots of different "intents," and the Constitution is a result of compromise between these intents. That is one of the reasons why anyone can quote mine the founders to try to find something that appears to back up there point.
Now, back to jar and Taz's point. Even if the founders unanimously had no intention of separating church and state, what does that have to do with us today? The founders have been dead for 200 years; they don't live in this country any more. We do, and it is our right (it is our duty, one might claim) to live our own lives under principles that we think are important.
Although Tom Paine wasn't a framer of the Constitution, his polemics were important in expressing a justification of independence from the UK, and he was quite clear the no generation is obligated to obey the promises made during earlier generations. In a sense, each generation is responsible for renegotiating the social contract that binds them together.
As long as we are on the subject of intents of the founders of this Republic, let's remember what I think are the important ones, that they, too, intended each generation to decide for itself how it will be governed. One point they had in mind is that the country was (and did) change greatly over the years. And, in fact, we aren't the same country that was founded over 200 years ago. One important difference is that the population is far, far more diverse than it was back then.
The second point that I don't think gets as much time as it should is that the founders themselves were well aware that, as one of the first to attempt to establish a constitutional democracy, they really weren't sure what they were doing. They realized that the document they produced was flawed, that whatever principles they were using hadn't been tested yet. And they were right. I flatter our ancestors in thinking it was a good first attempt, but it was flawed. Now, over that past 200 years of experience with constitutional democracy, between our federal government, 50 state governments, and the nations of Western Europe, we have a much, much better of idea of what will work to achieve our desired goals and what won't. (We probably have a better idea of what it is exactly what we want to achieve, but that is another topic.)
So our ideas of constitutional democracy, including the separation of church and state, did evolve over time -- just as the founders intended that it should.
To count as an atheist, one needn't claim to have proof that there are no gods. One only needs to believe that the evidence on the god question is in a similar state to the evidence on the werewolf question. -- John McCarthy
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