Pretty sure Duke’s “no exceptions” policy is a violation of this nurse’s constitutional rights.
Something tells me they would make accomodations if it were a Muslim requesting exemption.
Unfortunately, The Constitution is whatever Kagan, Sotomayor, Breyer, Ginsburg, and one other say it is.
Constitutional rights protect us from the government, not us from our employer. She may have a claim under anti-discrimination laws depending on what North Carolina's laws protect.