I think the trick is to make an effort to cover as many possibilities as can be dealt with by a reasonable effort (definition of "reasonable" varies significantly by context) when setting up something which you expect the general public to interact with. Not so much assuming that any given person has some disability you can't see, but that any large group of people will have at least a few.

Interactions with a specific person are another matter entirely, as you point out. There, I think the best you can do is roll with it if someone tells you that they're unable to do something without subjecting them to interrogation or scepticism

Very specific examples I have personally witnessed would include:

• People getting angry/irritated when they see young people exiting a car parked on a disabled spot without any obvious impairment or disability.
• People in public spaces (museums, tourist spots, etc.) taking it for granted that if they just saw you climb a few steps, that means you are necessarily able to climb 50 steps without any issues.
• When someone asks if there is a place to sit in a public building/area, staff/officials will often just answer "no, sorry" without considering that the person may actually really need to sit, even if they don't have a cane or something similar (in which case, they are often much more accommodating)

These are anecdotal, and specific to people I know and their disabilities, but I feel they illustrate how it's always good to just take a second to think about this sort of thing. It's also usually a good idea to just ask, instead of assuming.