Mother-in-law has moderate dementia and does not cover her mouth when she coughs. Is it rude to ask her to?

Funny, it should be ingrained in her brain. It would be a longterm memory thing. I see jo problem in reminding her but maybe futile.

In my over-55 community, many people seem to have never learned that they should cover their mouths and noses if they sneeze or cough. It's cough-cough here, cough-cough there, here a cough, there a cough, everywhere a cough-cough. They explode spit, phlegm, the lining of their esophagus, whatever, right out into the air that others breathe. I know we all learned proper sneeze-and-cough skills in elementary school to prevent the spread of disease. What happened that these folks think it's okay to spritz and spray?

Just be glad she's not spewing obscenities or racial slurs out of her mouth instead of coughing w/o covering her mouth!

Maybe you could get her some lovely, flowery hankies and give them as a gift, with the reminder that ladies cough into a hankie.

Otherwise, stand away and off center when dealing with her.

It may not be rude, but it certainly is pointless as your MIL's brain is now permanently broken and she will never retain what you say/ask anyway.
You may as well just get used to it, as I'm sure there are many worse things yet to come.
Hopefully she's not living with you and you only have to tolerate her behavior on occasion.

She won't remember. I'm sure she did it before she had dementia. I learned a lot from watching Teepa Snow videos on YouTube. She's an expert on dementia and caregiving and has excellent tips on how to better engage with our LOs with dementia for more productive and peaceful interactions. The only person who can change now is you, not her.

Certainly you can ask. With dementia it is unlikely she can compute and retain the information in your request over time.