In Kane v. De Blasio, (2d Cir., Nov. 28, 2021), the U.S. 2nd Circuit Court of Appeals held that New York City's COVID vaccine mandate for school teachers and administrators is not facially unconstitutional under the 1st Amendment because it is a neutral law of general applicability. However the court held that the process-- determined by an arbitrator-- for deciding whether a person is entitled to a religious exemption is unconstitutional:
The Accommodation Standards allowed employees to request a religious accommodation by submitting a request that is “documented in writing by a religious official (e.g., clergy).”... Requests “shall be denied where the leader of the religious organization has spoken publicly in favor of the vaccine, where the documentation is readily available (e.g., from an online source), or where the objection is personal, political, or philosophical in nature.”...
Denying an individual a religious accommodation based on someone else’s publicly expressed religious views — even the leader of her faith —runs afoul of the Supreme Court’s teaching that “[i]t is not within the judicial ken to question the centrality of particular beliefs or practices to a faith, or the validity of particular litigants' interpretations of those creeds.”
Bloomberg Law reports on the decision.