During the COVID era, it was very common to see signs posted outside of businesses and probably public buildings, saying things like:
Please do not come in if you are coughing, have a fever, or are short of breath.
The problem I see is that, whether it's the exact three symptoms above, or whether it's another, similar list, these are extremely generic symptoms that are quite frequent for people with asthma or with other common, but non-contagious diseases. For example, an adult asthmatic may be fine 95% of the time, but if they were just visiting a friend's house where several cats and dogs live, they may have a brief, minor issue with "shortness of breath" or "wheezing".
And it gets worse if they have OCD and are analytical. An individual like that might, for example, notice that their breathing is 99%, not 100%. (Of course, most people with OCD know and are perfectly able to just ignore the sign at that point, but it can make one flinch for half a second and be slightly unwelcoming.) So this not only affects people with common physical problems, but common psychological ones as well.
The bad thing is that these signs were practically everywhere during the pandemic - grocery stores certainly included - and things like the two conditions mentioned above are only example of a much larger list which affects a large swathe of the general population. But these conditions are not contagious, and they are often genetic. On the other hand though, they are also chronic.
Now, I want to highlight this: Common sense is common sense, and normally these signs would be ignored. However, if we use the example above about the cats and dogs, the asthmatic might cough a couple of times, which would be noticeable; but in this case, it does not suggest COVID, and the problem is something that is chronic. And while that's a temporary matter, they may be very slightly "short of the breath" all the time.
Despite being practically everywhere, were/are these signs and rules illegally discriminating against a large swath of the population with common, chronic, and non-contagious conditions?
To the extent a specific country is required, let's use the US and regulations like the ADA, though I'd be interested to hear about other countries as well.
The currently accepted answer (as of 2021-7-23, at which point it was the only answer) was a little hard for me to follow at first, because I believe there was some context I didn't see initially. Without that context, the rationale and flow behind the answer didn't seem to follow logically. In particular, when it was mentioned that people are expected to know the law, usually I think of that as mainly applying to the offender, as opposed to the victim. An offender can always still say or do something illegally though, and a victim's knowledge or ignorance of the law doesn't grant the offender a free pass to impede their rights. However with the proper context, the answer does seem to follow.
I could be misinterpreting something, but per a few comments back and forth, I think this is a rough paraphrase/summary, context included:
Basically the dividing line is a matter of how clearly the alleged offender is addressing the alleged victim. In the case of a typical COVID sign, there's typically supposed to be context that the sign doesn't apply to people who just have things like asthma, unless, for example, a store employee actually addresses the individuals directly. Therefore it is not clearly and unambiguously barring them for symptoms clearly attributable to asthma (or whatever the condition is). In this way, it is similar to how a "DO NOT ENTER" sign at the gate of a private property does not apply to friends and family who have previously been welcomed by the owner.
Also, the precise manner in which the sign is worded can weigh against this, but it doesn't single-handedly decide the case. However a "Please do not enter if you are <race/color/ethnicity X>" sign, for example, is illegal, because even in the proper context, it is still quite clear it applies to the people literally mentioned.