Healthcare is a contractual issue between you and the doctor of your choice. Get the government out of the education arena, they don't belong there, and only botch the process. Freedom for anyone to express themselves as they wish, with no restriction on First Amendment rights. One might ask how this conflict is avoided. It is really quite simple.
Libertarians are tolerant.
Those that are opposed to homosexuality have the right to disagree with it by teaching their children that it is morally wrong, and to belong to churches, schools, and organizations that challenge homosexuality. They simply don't believe it should be outlawed or have any special or marginalized legal status. By the same token, homosexuals in the party are free to believe and act in any manner which does not hurt any other person. They can send their children to schools which advocate gay issues, go to different churches, and belong to different organizations. They simply cannot force their beliefs on other people, nor obtain special legal status which marginalizes the more traditional legal status of marriage.