I live in upstate New York - one of the more aggressive states for COVID measures - and have not yet had to do this, a year and a half into the pandemic.
(I did, however, have to prove my vaccination status and present ID when I became a naturalized US citizen quite a few years ago. https://www.uscis.gov/policy-manual/volume-8-part-b-chapter-...)
> And for schools, didn't you used to have private schools or homeschooling as an option to avoid these kind of mandates?
These still exist.
But they don't get you out of the mandates anymore. Adults who already finished school used to never have to tell anyone their vaccination status to participate in society.
If they start spreading exponentially via aerosols, sure.
Constitutionally, SCOTUS has ruled on the point in the past. https://en.wikipedia.org/wiki/Jacobson_v._Massachusetts
> Jacobson v. Massachusetts, 197 U.S. 11 (1905), was a United States Supreme Court case in which the Court upheld the authority of states to enforce compulsory vaccination laws. The Court's decision articulated the view that individual liberty is not absolute and is subject to the police power of the state.
But covering the nose and mouth, when around others, is beyond the pale?