I don't think it's quite fair to say that any more than it is fair to say the Democrats are a party of nonbelievers. I think that the GOP is a party of social conservatives and that social conservatives tend often to be religious. So I would say that it's an organization made up of many people who are religious and want their values reflected in the laws.
I think one thing that is important to note is that it is only the really big issues (which don't really need to be seen as purely religious) on which the GOP acts that way. They are against gay marriage and abortion, but you can be against those (especially abortion) without being religious. On the other hand, the GOP is not really trying to push a complete religious agenda on the nation. They're not trying to make women submit to their husbands the way the Southern Baptists want, for example.
I'm no Republican, but I think that the fears of them creating a theocracy are overblown.