This issue doesn’t concern rights or civil liberties – there are no First Amendment issues in play, save that of the fact that public accommodations laws do not violate religious liberty as protected by the Free Exercise Clause.
Indeed, there are no issues in play with regard to any of the rights enshrined in the Bill of Rights; nor are there any 14th Amendment issues in play concerning state laws and local measures.
Unsurprisingly, you forgot the Ninth.
Forced association, forced labor - this is not freedom, no matter how you rationalize it.