In this play, you can determine the protagonist more easily if you identify the conflict of the play first. The conflict in The Normal Heart is not between two people, nor is between oneself and one's psychological qualities. The overarching conflict in this play is between Ned and society. Ned sees a problem and investigates it. Ned identifies the problem and, with the help of Emma, sketches out a first step for ending or at least controlling the problem. Yet, with this knowledge and wisdom, Ned cannot get any segment of society to agree with him and to pull for and implement the first steps of the solution, which is for gay men to abstain for sexual encounters.
It should be more clear now that Ned is the protagonist while society, in its several different represented parts (family, government, male gay community, gay friends, news media) is the antagonist. This sort of conflict is identified as Self against Society, and in the definition of this conflict, Self is the protagonist while Society is the antagonist: Ned against society.
"We're all going to go crazy, living this epidemic every minute, while the rest of the world goes on out there, all around us, as i f nothing is happening, going on with their own lives..." (Ned speaking)
protagonist: the leading character, hero, or heroine of a drama or other literary work.
antagonist: a person who is opposed to, struggles against, or competes with another; opponent; adversary.