@ Mikey I agree that religion is important in the US, but as far as the official machinery of state is concerned, they are avowedly secular- church- state separation is alive and well, unlike here in the UK with out cohort of unelected bishops sitting in the House of Lords. etc.
Much of the religious observance at council meetings in the US - prayers before starting, that sort of thing - are being challenged, and are I think technically unconstitutional ( although I might have that wrong). Indeed, there is no constitutional reason why the President needs to swear an oath to god on the bible, as they currently do - but it has become a tradition.
And you are of course right that it is more likely that, say, a muslim or a hindu is more likely to be elected ahead of a self-declared atheist.
That is slowly changing though- religious observances in schools, in courthouses and other state institutions are regularly challenged, and there is an increase in self-declared agnostics/atheists/no religion individuals, as evidenced by a recent survey...