Keep in mind that both sides in this case are relying on the First Amendment … but different “rights” protected by the First. Coach is arguing that his praying immediately following a game, on the field, is protected free speech, and by prohibiting him from doing so, the school district violated his right to freedom of speech. The School District is relying on the Establishment Clause of the First, i.e., the clause that prohibits the establishment of a “state” religion.
For me, this is the crucial aspect of the case. The coach was not fired because of the content of his speech, i.e., prayer. Rather, he was fired because the school district had been advised that allowing this to go on could subject them to civil lawsuits by students and their parents, claiming that the practice violates the Establishment Clause. They made every effort to accommodate the coach’s wish to pray following games. “Free” speech has never been absolutely free: the whole “yelling ‘fire!’ in a crowded theater thing. Speech is always subject to reasonable limitations as to time, place, and manner. The thing that makes it hard for the coach to win (I think) is that there is no evidence that the school district acted because of the content of his speech, i.e., a prayer. If this truly was only about the coach’s freedom of expression, there would be no problem with him doing it in the privacy of the coaches’ locker room, or on the field after the students had gone, both of which, IMO, would represent reasonable time, place and manner restraints on his protected speech, and both of which were offered as alternatives by the school district. But, as the following article points out, it depends which version of the facts you believe. https://today.law.harvard.edu/supreme-court-preview-kennedy-v-bremerton-school-district/
Although this is a Q & A with a Harvard Law Professor, it’s easily understood by non-lawyers, and presents a very clear and concise overview of the case, and explanation of the issues involved.