There are alot of neocons around these parts starting to use the "L" word, who really ride on with learned societal or religious memes without a basis in rational principle.  Sometimes labels are just labels and you have to see what that person is really all about.  On balance, I would think libertarians would be most accepting of trans-gender, but probably like with just about anybody aversions to the unusual and new must be overcome.

I think that people in general find the unusual to be scary, but this works itself out over time if there is liberty.  I tend to look for evolutionary reasons for aspects of human behavior and I find it helpful to think about the hunter gatherer clan background I believe mankind came from.  It's reasonable to assume that clans/families from similar regions would develop some amount of trust and preference for their own clan since they are the most mutually invested in systems of exchange and support among each other and posess intimate knowledge of each other's principles of behavior.  Enter a member of a completely unknown tribe onto the clan compound and the tribe members will get a little freaked out.  This person is a question mark and there is reason to proceed with caution in dealings with them until their nature is revealed over time.  Then acceptance eventually occurs and life can proceed without mistrust and suspicion.   A transgender person is not something most people probably encounter (at least not where I live) so I bet there are going to be uncomfortable feelings to be overcome.

Have we not seen this in many areas of racial/gender/ethnic/religious tension?  These changes take time and come very slowly, or not at all outside an environment of liberty.  It was Thomas Jefferson who took the inititative to eliminate the death penalty for homosexuals in Virginia and reduce the penalty to mere castration (I guess it was a start).

I think the environment of liberty is critical to this process of dissoving destructive barriers to interaction and diversity.  To maintian irrational biases deprives the individual of beneficial relationships that serve life.  Once it's accepted that authoritarian leaders are to determine what is acceptable, your just done.  The beasts of bias always step up and grab the gun to start to lead the people astray.