Paul Clement's Reply Brief (12/21/21 re cert petition) is terrific (one of America's best appellate lawyers). It helps the coach that the prayers occurred after the game. Copying from the Reply brief, this is the key argument in favor of the coach:
Nor did Kennedy lose his right to pray because others chose to join him on the field and engage in their own personal expressions of faith after the district suppressed Kennedy’s religious exercise. That was of course their constitutional right, not any form of government speech. See, e.g., Tinker v. Des Moines Indep. Cmty. Sch. Dist., 393 U.S. 503, 506 (1969). That showing of solidarity was also an entirely predictable consequence of the district’s suppression of Kennedy’s private religious speech. Intolerance of private religious speech is neither popular nor constitutional. The sensible and lawful course for the government is neutrality, not hostility to private religious expression.
Of course the government may discipline “a geometry teacher” who “converted her classes into partisan political rallies” or a “court clerk who sang showtunes to litigants.” Those are obvious examples of non-germane speech occurring “within the scope of an employee’s duties.” Lane, 573 U.S. at 240. A public employer need no more tolerate such speech than it need tolerate a football coach who used timeouts to talk trigonometry or the infield-fly rule rather than gridiron strategy. Here, by contrast, Kennedy’s prayer did not occur within the scope of his duties; he sought to pray only after games concluded, after the customary handshake with the opposing team, and after students were separately engaged in other postgame activities like singing the fight song. The district cannot convert that private religious expression into its own speech by pretending that Kennedy claimed a right to do something else entirely.