I left an opened jar of mayonnaise at room temperature for 22 hours. Is it still safe to use?

By opened, do you mean the lid was off? I think it's still safe, as room temperature is certainly no threat, unless some bug or fly got into it. But toss it if you're worried, or just put it back in the refrigerator as soon as possible. Even more deadly than being left out and open would be if some human stuck their finger in it. Human hands are the worst contaminators of all time. They touch EVERYTHING and are not washed nearly as often as they should be. Especially before handling food. I worked in a restaurant that produced a lot of cold, unheated food, and we had to wear gloves at ALL times. One finger coming in contact with any food that would not be heated could contaminate the entire batch. Even washing cannot remove all microbes on the hands for long.

I suspect the concern has been ingrained for many years, and likely is a holdover from when the eggs in mayonnaise were not pasteurized. That would explain the fear of food poisoning from salmonella, and perhaps even E.coli. I did food and facility inspections for many years, helping to trace the sources of food borne illness. And I don't recall even one time when we could definitively say the source of the trouble was the mayonnaise. There are just so many other sources of contamination which are more likely the culprits than the mayo- but of course that's not what some folks can hear. Nobody wants to think that their fridge, their hands, their bowls or utensils, or their own hands could be responsible. Or that maybe it's one of the other ingredients, because of course, it couldn't possibly be the romaine lettuce or the bag salad greens, now could it? Or the cutting board that is filled with deep nicks and cuts. My own mayo is refrigerated, and it's what I'd recommend to others - but there is best scenario and practice, and then there is real life. Real life means weighing up the risks and using the brain, knowledge and experience you have, plus a bit of research as need be.

Growing up, my mom never refrigerated her Helmann’s Mayo. Never got moldy; never made us sick. I feel that people go a bit overboard on some of these food safety issues, but do whatever makes you feel comfortable.

I grew up in the Deep South and we
Never ever refrigerated mayonnaise - (our house was not even air conditioned until the 1970s.) As we all know Mayonnaise is the perfect vehicle for bacterial growth - but by itself, cannot cause food poisoning.

Throw it out. It doesn't cost that much and how would you feel if you got family or friends sick 💔 toss it and be safe.

Have you ever had food poisoning?

Well, that's complicated. I presume we are discussing commercially made mayo? Although mayo is usually portrayed as the bad guy inflicting food poisoning on the unwary- it actually works to inhibit bacterial growth. It's the acidity, for a start - and the preservatives which are added to - get this - inhibit bacterial growth, to lengthen storage life. But, yeah- 22 hours at room temperature, not sure I'd want to risk that. I guess you have to weigh up the other associated risks. Was it a relatively new jar? As in how much already introduced contamination was there? Was the lid on? What do you consider "room temperature"? Because there is a big difference between 68 and 78F, obviously. If you just can't bring yourself to toss it, may I suggest you use it in an alternative manner. Use it to make a wonderful chocolate cake - which will use about 1 cup of the stuff.

This has happened to me before (more than once).
Both Antonia.James and Nancy are correct.
BUT
I am cheap, so when I happened to me, I stuck it back in the refrigerator and ate it and didn't die.
OTOH, would I do it if it were outside and 80 deg? Nope

I would definitely not use that mayonnaise - even if "room temperature" were fairly low, say, in the 50's or low 60's degrees, Fahrenheit. It's just not worth taking the chance of getting sick. ;o)

Two opinions.
Yes. No.
You pays yer money, you takes yer choice.
https://www.epicurious.com/ingredients/the-truth-about-mayonnaise-and-food-safety-article
https://www.stilltasty.com/questions/index/203#:~:text=Answer%3A%20You%20can%20let%20an,8%20hours%20should%20be%20discarded.