Seeking to compel conformity through the force of law violates the libertarian principle that we should leave others alone unless/until they trespass against the person or property of their fellow man. Thus it's not a libertarian position.
There is a huge distinction between compelling conformity and having the public define what is acceptable in public behavior.
Yes, I support having a third bathroom available for transgender people instead of having mutilated males go into a womans restroom, but segregating the genders in restrooms is an example of forcing people to conform to the expectations of others. If you want to mutilate yourself, that is your twisted preference, but dont compel the rest of us to be exposed to your perversions.
Hence Libertarianism is actually at war with Conservatism, not an ally of it or version of it.