"I suppose what I'm trying to get at is what compels these groups of people to passionately defend their beliefs against say an Atheist or Muslim, but let it fall to the wayside when it comes to politics?"

I think, in the realm of politics, most people care more about POLICY than the gender or religious denomination of a representative. I mean, most voters do seem to demand that they want someone who claims to be religious, but as long as they support the policies a voter likes, their actual belief doesn't seem to matter that much. Take the current "controversy" over the lack of women in elected political positions in congress. The reason people didn't really want Sara Palin wasn't because of discrimination, and even feminists wouldn't vote for her simply because of her gender, it was all because she did not represent the views of the people voting.

"Obviously a good part of these groups want America to become a Christian Theocracy. Candidates like Ted Cruz and Mike Huckabee have basically stated they would rule America according to the Bible. Yet they are currently supporting a man who struggles to answer questions according to the Bible or religion. I find it as a fascinating occurrence of cognitive dissonance, but what do you think accounts for this?"

Even religious conservatives don't REALLY want a theocracy. Perhaps, subconsciously, they realize the fact that they don't really appreciate many of the religiously inspired laws we are routinely dealing with now. Want to buy a twelve-pack but it is eight o'clock on a Sunday? Too bad. Many of them do, on some level, realize that a true theocracy would probably effect them more than the average atheist.