I take it you have not read the Constitution. God is not mentioned therein. Not even as "the Creator", or even "Nature".
You were perhaps thinking of the Declaration of Independence? That does show that while the Government of the United States was not intended to be, nor is it, religious, per se, the Country of the United States was founded by and for those who believed in "Natures God" and "The Creator", and belived that our rights are "endowed by" our "Creator". However several parts of the Constitution, the first amendmenet and Article VI paragraph 3 for example, make religious discrimination, by the government unconstitutional. It also forbides interferance with Religion. It does not however forbid persons with religious motivations from trying to influence or become part of the government. That of course includes both majority and minority religions, however those might be defined or determined.
But the Constitution is a contract and it clearly states that "No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President". Given that there is considerable information, including Obama's own books, that he is not a Natural Born citizen, no "conspiracy" is required of those wanting the Constitution enforced as written.
It is a conspiracy theory. That many birthers contend Pelosi is aware of his non natural born status and isn't doing anything about it is a de facto conspiracy, or that the Dept of Health in HI is hiding his BC also makes it a de facto conspiracy theory.
Obama released his BC in 2008, factcheck.org reports they saw it, examined it and said it was good. The HI health minister saw it. There is no mention in the Constitution of a long form or short form being necessary, the state of HI doesn't even issue a long form anymore (in any case it only contains additional geneological information and is not necessary to prove citizenship, only the place of birth is necessary and it is clearly Honolulu). Even that law that says non residents can get a HI BC doesn't really prove anything, the law clearly states that your place of birth is listed even though you have a HI BC, To use an example from the dept of helath, if you were born in Bali your birth location is listed as Bali, not a place in HI.
This issue was taken care of during the campaign, everyone except a few have moved on from it. We may not like him for what he's doing, but attacking his citizenship isn't the way to go about opposing him, in fact it hurts the movement by tarring everyone as crazy.
Marxist? Yes. Socialist? Yes. Corrupt? Quite possibly. But is he allowed to be President? The only reasonable answer is yes, he was voted in, and confirmed.
Thats the last I'm saying on the issue, if by now people aren't convinced, its because they don't want to be. I've moved on, I suggest you do to.