I think some countries require that the terms of employment be somewhat related to the nature of the work. Contraceptives might be banned by that. (IANAL, just someone who's had this explained by a lawyer.)

In a fully remote company, where you never meet customers, vendors or other employees, requiring vaccination might be viewed by a court as unrelated to the work. If you're supposed to meet customers or other employees and there's a pandemic going on, though...

What about requiring exercise or fluorinated water? Those neither invade privacy and improve things for people and the company.

There was a case her in Denmark (which, normally, have much stronger employment laws than the US) where it turned out that a company could require its workers to exercise (and they were computer programmers, so it wasn't directly related to their job) provided that it happened in working hours.

The military and sports teams certainly mandate exercise (explicitly in the military's case and at least implicitly but very likely explicitly for sports teams).

Military pilots are also issued "go pills" (dextroamphetamine) for long combat and long single-pilot transit sorties.

The military is quite different. You more or less, in colloquial terms, belong to the government who promises to be a good guardian.

There isn’t much you can say ‘No’ to without risking a discharge or courts martial.

> requiring exercise

I'm sure you could, if you paid the employee for it.

> fluorinated water

How would anyone verify that? Seems like the kind of thing you'd have to go to court to find out if it's legal.