Yes, I know they obviously currently can, but I would fight to make it as hard to enforce as possible. With so many rules, training, litigation, opt outs, extra accommodations having to be made, etc, that it just isn't worth it moving forward.
We basically had millions of people forced in masks by their employers on a whim, without the employer knowing a single thing about masking, their pros or potential cons, training on how to wear them, their efficacy, etc. Without considering disability protection such as hearing impaired, or hard of breathing. Without making accommodations for those who feel oppressed, or have social or psychological downsides such as anxiety or depression, communication issues, physical issues ranging from as small as rashes or acne, to permanent damage behind the ears, etc., associated with mask usage.
It's just hard for me to accept that anyone can make you do something that might have downsides, without their research of those downsides, and appropriate accommodations or exceptions in place. This is a slippery slope for us to go down. Even for those of us normally rooted in capitalism.
When it comes to protecting employees rights, we have done this before. For example, forcing people to wear politically or religiously oppressive items. An employer can't just force someone to wear a swastika symbol, or a Christianity reference, or a republican or democratic reference. For masks, they already can't force N95 wearing without proper training classes(which I know of many who have just bypassed this fact). Why not all masks? Make it as hard as possible for a business to actually enforce it, to where it just isn't worth it for most. Can they force everyone to wear 7 N-95 masks? I mean, it's their place of business. To hell with passing out from lack of oxygen. It's the employers right, correct? A weighted hat on their head that might cause neck issues just because it's their place? Wear 10 sweatshirts even if it's 100 degrees in the office? I know these are silly, and hyperbole, but you can easily see why someone would question what an employer can truly force one to wear or not, and when it might be appropriate to take legal action to protect against it.