So marriage licenses grind to a halt when she is on vacation, in hospital, on mat leave or in prison? There must be some clause about who fills in for an absent official?
IANAL, but my guess…
Presumably the boss can make office-related rules - “in deference to our employees who are fasting for religious reasons, there will be no food or drink consumed in the office.” But she cannot tell you that you can’t slip out for a quick burger at lunch. (Unless you don’t get lunch, which I presume is contrary to any states’ labour standards.) She sure as hell cannot tell you what to do outside business hours, especially what to eat or what to do on your day of rest.
In fact, the employer cannot discriminate against you for religious reasons; since religion IIRC is a protected class; cannot refuse to hire non-Christians, or Catholics, or Episcopalians or Muslims etc. Similarly, cannot fire you for failure to follow rules that discriminate. Presumably part of your (paid) employment duties could include attending a religious service, but if that conflicted with your beliefs then that would be a violation too. However, there are not too many religions that make it a grievous sin to attend another church in observer capacity or as a courtesy, etc. Many churches strive to encourage inter-denominational cooperation. Your paid duties presumably cannot force you to participate in the rituals, (especially circumcision).
There are basic tasks that any job involves. If you cannot interact with women dressed in a normal fashion for that business setting, then presumably you took the job under false pretences since you cannot do the job as it is defined. You cannot claim religious discrimination when let go. Of course, the employer must make “reasonable accommodation” so if there is a separate line for men-only that you could reasonably work on, say, then that might be the correct compromise. I can’t think of too many places like that outside of a steam bath business.
The opposite is different - unless there is a deep and serious reason, the employer cannot require their employee to remove their head-scarf. Say, they are working around power tools and risk of tangling in the machinery… but then, a properly secured scarf, not flopping free, is probably no more dangerous than an open-collar shirt or long hair, which should be similarly restrained. “Reasonable accommodation”.
“Wrongful dismissal” is the term for firing someone without just cause. However, in the land of the free, workers have no rights - so as long as the firing is made “because we don’t get along” and not due to failure to obey an illegal order (prove it!) an American employer can do all sorts of nasty things not permitted in the civilized world because America has “employment at will”. (Wiki says "Common law protects an employee from retaliation if the employee disobeys an employer on the grounds that the employer ordered him or her to do something illegal or immoral. However, in the majority of cases, the burden of proof remains upon the discharged employee. ")