I’m not sure. It would depend upon the employer.
My point in bringing up these conflicts is that sincere, moral objection goes both ways . . . and there doesn’t seem to be a legal framework to give agnostics and atheists parity with the theists in these types of disputes.
The idea that overshadows this whole discussion is the conviction that atheists lack a moral compass . . . so we are not entitled to claim the moral high ground when I object to participating in gay conversion therapy, or when I object to giving dangerous drugs to pregnant women to prevent them from having a lesbian.