Don't they want the church intermingled with the government? I mean, Maybe there are some low teir libertarians out there who would be happy with the church running the government, but I can't say that that really falls in line with libertarian values.

Assuming they are willing to stick with their libertarian values once their guys get into the government. Power corrupts, and all that. but as an Ideology, I just don't see how it could work.