Wtf, dairy mayo? Is this an american thing? Mayonaise is oil, egg yolk and optionally mustard/garlic/spices/flavourings.
Why? US eggs are stored, shipped, and sold refrigerated. For logistical simplicity, they're usually kept in the refrigerated dairy section of our grocery stores. We do that because our eggs have their natural coatings washed off and they are given a light (pretty much imperceptible) coating of mineral oil. While that does slightly reduce the liklihood of contact cross-contamination from our filthy poultry supply chain, it makes them more susceptible to spoilage— though they're generally fine for extended periods at room temp as long as they stay dry... but restaurant health inspectors sure as hell wouldn't tolerate it. (Some people actually immerse them in mineral oil to preserve them for much longer, though I have no clue what the comparative time to spoilage would be.) Last I checked, there was a 1 in 10k chance of an egg having enough salmonella (et al) to sicken a healthy adult if eaten raw, but the FDA went on the offensive at some point in the 70s or 80s admonishing people not to eat eggs that weren't fully cooked, eg. with runny yolks, so now diners that sell bazillion "over easy" runny fried eggs, and even some bars that make you any sort of flip or other cocktail with egg whites, legally has to put a disclaimer on the menu saying that it might cause foodborne illness.
You can always get cartons of egg whites, and less frequently, whole shell eggs that were pasteurized slowly enough for them to maintain the physical properties of raw eggs without the slight pathogenic risk— very handy feeding or serving egg drinks to more suseptible folks, such as the elderly, immunocompromised, or children.
Side note: I very much love pasteurized carton eggs. Pre-separated, no guessing the size ("my recipe wants 3 medium eggs, i only have large, do I use 2.54?") and peace of mind when making stuff like fresh mayonaise.
That said, I've made mayonnaise with unpasteurized US shell eggs literally thousands of times, tasting every time, and eaten it at restaurants hundreds of times. What anyone considers "safe" is relative. Fine dining restaurants across the globe sell millions of portions of it per day, as they do beef tartare, carpaccio, sashimi, French style buttercream and meringue, raw oysters, clams, flip cocktails, and zillions of other 'unsafe' things. US restaurants must sell tens of millions of runny-yolk eggs, and millions of Hamburgers not brought to 145 degrees internally.
They don't do so entirely without incident, but it's well within many people's risk tolerance threshold. Surveillance for outbreaks of serious strains (eg Salmonella Heidelberg, E. Coli OH157, etc) is pretty good— people usually seek medical treatment when the serious symptoms start, most GPs and emergency medicine practiciners are pretty good at knowing when they need to test, and epidemiologists do follow up before they even hit the requisite 3 cases to be considered an outbreak.
"*Pasteurized eggs have been heated to a high enough temperature for a long enough time to kill Salmonella."
Only 3 percent of the eggs sold in the US are pasturized though and if you make mayo with ordinary eggs, salmonella is a possibility.
There’s a pretty close association between such products and eggs, so I can understand why people might try to use the same label.
But ultimately I think this is just causing confusion and pointless side discussions (like this one!), so it would probably be better if we dropped it.
And in this context specifically, it should be evident that regular mayonnaise isn't vegan, since vegans don't eat animal products. Which includes eggs!