I believe that if one's morality doesn't derive from Biblical principles then I'd be hard-pressed to assume that one would have the morality needed to govern a nation founded on Christian principles and I certainly wouldn't trust anyone who outwardly rejects those principles.
I have to trust Christians even though their morality isn't what I'd call "complete".
For instance, I believe calling people names and using personal attacks is a sin. Christians don't agree.
I still wouldn't legislate my morality over the morality of the community.
Why isn't political ideology enough for you? You know, how one stands on the issues.