Second, the hypothetical store/service/place could theoretically provide a number of auxiliary aids and services to eliminate the risk.
They could. But they don't have to. They are not bound by the ADA, or anything else, to offer you the accommodation you request. They merely have to give you a reasonable one.
What you just quoted is exactly why the store can't simply tell a person to wear a mask or leave (without offering alternatives; if they claim they have a disability; insert qualifier here).
Um, would you go back and please check where anyone other than you suggested that course of action for the business? Because, I'm pretty sure you won't find it. Which would mean that you are engaged in a strawman argument. Maybe bring yourself around to what we are actually saying, hm? Thanks.
So, if a person refuses to wear mask but is otherwise well behaved, what happens?
"I'm terribly sorry, but there's current orders/regulations about wearing masks in public places. We have to ask you to remain outside the building. How might we otherwise meet your needs?"
The store doesn't actually have to ask you any questions about what your health issue is. It is irrelevant, a boogeyman.
If they ask the wrong questions they can get sued.
Having spoken with a friend of mine who works in disability rights, this is not quite correct.
Technically, they can ask. What they cannot do is require an answer as a condition of service. If they ask, "Sir, could you tell me what your issue is, so that I can help you better?" they are not subject to suit. If they say, "Prove to me that you need that service dog, or you cannot come in!" then they are in trouble.
If that person is lying, the store can be sued anyway, and the store will have to wait until the case goes to court to find out if their suspicions about lying are correct. Or, the minimum wage employee can just shrug and walk away.
You continue to miss how this is not an all-or-nothing, give them full service or none situation. "Sir, if you can give me a list of the goods you need, I'll get one of our staff to gather them up and bring them out to you," is a perfectly reasonable accommodation for retail services. So is, "Please see our website for ordering." And so on.
I really suggest you not continue to miss this.
If lawsuit is your boogeyman, there's a couple points to hit:
1) There's a limit to how much this suit is worth. They cannot bleed you dry for this, and in fact, unless a pattern of behavior of not accommodating people with disabilities is established. A first offense generally gets you a warning and orders to change your policies or establishment to deal with the issue properly. So, one yahoo will generally get you a visit from a bureaucrat, not a hundred thousand dollars in the hole.
2) With a mask order in place, if the proprietor lets someone in without a mask, they technically suffer legal exposure from everyone else on the premises, who is now being put at risk. If any of them come down with covid-19, they have grounds for a civil suit. If anyone dies and that is connected to your establishment where you didn't follow the rules, now you may even have a wrongful death suit on your hands.
Thank you, the threat that a yutz trying to weaponize the ADA is paltry compared to the millions you may be on the hook for in a wrongful death suit.