I can only speak for myself, but it certainly impacted my relationship with my employer. Aside from it feeling intrusive into my personal health choices, It seemed to be an extreme ultimatum that reframed the power dynamic and how they valued me as an employee.

An apt analogy would be if your husband/wife threatens divorce because you left socks on the floor. Even if you don't mind picking them up, or were planning to already, it is shocking and damaging that they would go straight to the nuclear option.

Flip-flopping on the issue almost makes it worse. If you were willing to fire/divorce me yesterday, and don't care about the issue today, how much do you really value me and our ongoing partnership.