Good = God.
I see we’re getting the usual confusion about what many if not most people who call themselves “atheists” actually mean by the term. An Introduction to Atheism from the Secular Web discusses some of the different meanings of “atheist” and “agnostic”.
Of course it’s certainly possible that Jefferson, if he were alive today, would call himself an agnostic. (Or maybe he would still be a Deist. Or maybe even a Christian–our scientific knowledge about the origins of life and humankind, and non-theistic philosophies like secular humanism, have advanced since Jefferson’s day, but so have the ideas of liberal Christian theologians. Or he might be a Buddhist for all I know.) On the other hand, a 21st Century Jefferson might very well reject the dogmatism of asserting that “it is impossible to know whether there is a God” in favor of simply disclaiming any current knowledge of any evidence or adequate argument for the existence of a God or gods, and so he might call himself an atheist rather than an agnostic.
To address the OP’s question, here’s a site on Jefferson’s religious beliefs.
My own guess is that, if you could bring TJ to the present as the OP describes, his religious beliefs would be pretty much what they were during his natural lifetime.
MEBuckner addressed this some already, but I’d like to add that I consider myself an atheist, but I realize that proof in the nonexistence of God is impossible. By your standard, there would be no atheists that I’m aware of.
My own take on the definitions is that an agnostic isn’t sure, but finds the idea of a God to be somewhat plausible. I think it’s highly implausible, so consider myself to be an atheist.
And yes, I’ve always thought that 18th century Deists would likely be atheists today, since the only difference I can see in the way we arrived at our beliefs, is that I have access to science that explains how the world around us could have come to be naturally, without a supreme being, and they didn’t.
You still have no evidence of how it all began though, where it all came from. Are we to believe all the matter in the universe has always been there? Was it not created some how? The Big Bang doesn’t explain this, it just explains how it was all distrbuted. Anyways I don’t want to get in such a debate here I’m just pointing out how modern science doesn’t erase a certain fundamental question of, “How?! did this all begin.”
Anyways, I’m not saying you have to have proof there is no god to be an atheist. I’m just saying I think some people would need such a proof before they called themselves atheist, I think TJ may be such a person.
It’s also not impossible I guess he’d have the same religious beliefs he had in life, hard to say with a question like this.
OK, so from what we have here, a modern TH could be:
- Still a deist
- An Agnostic
- Of a very liberal branch of Unitarian Universalist.
- A Humanist Atheist
In any case, he would STILL be accused of being an atheist in the negative sense of the word, and his non-belief in the orthodox J/C God would maka a Jefferson election virtually impossible.
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But yet somehow I suspect that even if (4) were the case, a modern Atheist Jefferson would not be a shrill, proselytizing “handstabber”, the kind to use derisory put-downs about “invisible pink unicorns” or “magical sky pixies” when making his arguments for how come believers are in error.
Jefferson was accused of being an atheist back when that was more stigmatizing than today, so I don’t think his religious beliefs would keep him from being elected in the present time.
Not necessarily. In the election of 1800, in only 6 of the 16 states were presidential electors chosen by some sort of popular vote; in the election of 1804, it was up to 11 out of 17. I believe it’s only when we get to Andrew Jackson that you begin to see the modern idea of the Presidential election hinging, albeit indirectly, on the outcome of a popular vote.
This isn’t what is meant to be a Deist in Jefferson’s time. The deists largely believed that it stood to reason that the world had to have been created by some master craftsman. This wasn’t an article of faith to them: it was something they felt stood to reason.
And I have a hard time understanding the above sentance. “I see a hard time?” 
There is nothing to “buy into” with atheism. You simply stop “buying into” the idea that there must have been a creator.
Perhaps, but deists tended to be skeptics, not fidelists.
It seems to me that philosophy has progressed somewhat, in that we no longer trust in easy parochial things like our own terrestrial credulity to guide what is and is not possible. Thus we can more comfortably say, with regards to the universe, that we simply don’t know, and the issue may even well be beyond our understanding. At the very least, bizzare new findings like the idea that, at least if string theory is true, there is no way to shrink the universe down to a point: past a certain size, due to the oddity of having a bunch of extra dimensions, shrinking from one perspective is actualy growing from another perspective. It’s stuff like that makes talking about “beginnings” seem like an absurd extrapolation of everyday concepts to events that are far from relevant to our everyday understandings of things.
Maybe, maybe not, but we no longer assume that such things would require a creator.