Second, even if a public accommodation law did ban such discrimination, it couldn’t apply to parades organized by nongovernmental organizations. Such parade organizers have a First Amendment right to exclude groups from their parades based on the messages the groups convey about their members’ sexual orientation, political affiliation, religion, race and whatever else to make sure that a parade conveys just the speech that parade organizers want to convey. That’s what the Supreme Court held in Hurley v. Irish-American Gay, Lesbian, and Bisexual Group of Boston, Inc. (1995), when it said that the organizers of Boston’s St. Patrick’s Day Parade had a First Amendment right to exclude the gay/lesbian/bisexual group. And the same applies here.
Thanks to my student Ashford Kneitel for the pointer.