@david no your employer does not have the right to fire you for not participating in their religious practices. The only concern of your employer should be whether you do your job, in the US, you cannot discriminate against perceived, past or future disability or health condition. Otherwise your employer could mandate that all women get abortions, or that all men that work with children have their genitals removed. If it’s safety that you want, then remove yourself from society altogether.
Although, I do think stores should have the right to mandate things on their property, there are laws that say they cannot discriminate on a variety of reasons. If you want to mandate that stores service gays and transgender, they should be mandated to service those that aren’t woke.