I'm fairly liberal and usually vote for Democrats
The Republican Party seems to be made up of three fairly distinct groups:
1. Libertarian, fiscal conservative: least government, less spending, less taxes. In general, this group should at least tolerate crossdressers and LGBT people.
2. The pro-business: this group is mostly out for preserving privelege and increasing wealth. Usually claim to want to reduce regulation, but mostly want regulation and policies to favor their particular interests. Will switch to the Dems when in their interests. Only interested in moral issues when they can make alliances; otherwise only interests are financial.
3. (mostly) religious right: interest is in imposing their view of morality on everyone else thru the force of law. Want to give more power to the government if the government agrees with them. Typically believe that crossdressing and gay behavior is sinful and should be illegal.
I know these are generalizations (Max Weber might call them "ideal types"), and that most people would really have a mix of these beliefs (even if self-contradicting), but this is how I see the Republicans now, and these contradictions are tearing them apart.