Companies aren't restricting any of those. But they can require you to wear a mask to patronize their establishment.
No different than taking a charter boat for fishing or pleasure. Policy is wear a flotation device. No device, no charter.
There a plenty of examples where you must don certain protective gear to participate in or access certain activities or venues. Businesses and venues get to decide what their policies are.
Bottom line it is private property rules - and in this environment - good luck fighting it without a documented handicap.
Even so, you cannot force your way in and win.
I went to the Verizon store. About 10 feet in, I was confronted/greeted, told no mask, no entry. I told them I have a documented medical condition that prevents me from wearing one. They had me step outside and we took care of my business there. Had it been something that couldn't have been handled just outside the doors, they told me to contact customer service or use the website. It did not appear to be a battle that I was going to win. And taking it up legally, they are going to simply stick to that tack and prevail.
Now, a grocery store or 'essential to life' business, pharmacy, doctors office, etc; could be a bit more problematic for them.
It's a partially gray area, but public sentiment and mob rule are currently the order of the day.
You're going to be asked to leave - and if you refuse, you will become a social pariah, will likely be filmed and go viral - and may enjoy some time with LE.
Here's an old story that may help to understand herd mentality while we hope for herd immunity:
There was an experiment involving five gorillas who lived in a large cage. The cage had a ladder in the center, and everyday a fresh set of bananas where placed high up on top of the ladder.
As soon as one gorilla would attempt to get the bananas, the scientists would spray all the gorillas with cold water. This process was repeated when any gorilla tried, and eventually, the gorillas stopped trying to get the bananas.
Some time passes and the gorillas left the bananas alone. At this point, the scientists stopped spraying the cold water and replaced one of the five gorillas with a new one.
As soon as the new gorilla sees the bananas it attempts to climb the ladder. But this time, instead being sprayed with cold water, it was the other gorillas that attacked him and prevented him from getting the bananas! They didn't want to get sprayed with cold water again so they made sure that the new gorilla stayed away from the bananas.
After a couple of attempts (and attacks), the new gorilla learns to leave the bananas alone.
The scientists then replaces yet another gorilla. The second replacement does the same thing as the first new gorilla and it too gets attacked. Amazingly, even the first new gorilla, who know nothing about the sprays, takes enthusiastic part in the attacks.
The process of replacing gorillas is repeated until all the five original gorillas have been replaced with new ones. Each time a new gorilla attempts to get the bananas, it gets viciously attacked by the other gorillas.
None of the gorillas in the cage knew why they shouldn't be climbing the ladder, yet none of them would try again, nor would they allow the other ones to do so.
Their only reason for their behavior is that its "Just the way things have always been done around here".