Less well-known writers did manage to get plays about gay characters produced on Broadway. Even the rather well-known Goetzes got one produced but I suppose being a married couple may have made them feel safer about it. (And you can't get more hetero than Billy Rose, who produced it.) The plays tended not to be particularly happy plays, but there were plays focused on gay or bisexual characters and relationships. There were not many but there were some. I can't believe there are no books in which these plays are discussed.
Are you saying that Lunt and Fontanne were definitely gay? I think they may have been. Certainly Margot Peters in her book about them seems convinced of that, especially Lunt, but the evidence she presents is far from conclusive.