How do Cats Know Who is a "Cat Person"?

The person who feeds the cats is probably a cat person.

I’ll tell you a story…I fostered and then adopted a cat with a “history.” she bit me frequently and it took me quite a while before she wasn’t suspicious I was going to hurt her or be rough. She would bite anyone who approached like they would a dog…the Jolly Hello type of approach. I had to hire a cat sitter, and was told she was a “cat person.” Uh huh. The lady came for a get to know you visit and I told her that cat bites. She immediately tried to show me how wrong I was and went at the cat in the Jolly Hello like you would a dog, and got bitten. I said, " I TOLD you that cat BITES." So IMHO it is how the person approaches the cat the kind of results they get, and it’s not that cats can tell if someone is a cat person but whether the person knows how to approach a cat, and respects its right to say not right now thank you. (BTW the cat sitter did win over the cat over the course of a week.)

Not being able to ask the critters makes it hard to know. Everything is supposition. But there are clearly some behaviours a human can engage in that make cats feel more comfortable. Desmond Morris’ Catwatching made a specific point that behaving like a contented cat can make nervous cats feel less nervous. So yawning, and acting like you are cleaning yourself can make a skittish cat think that you are clearly totally contented and not looking for a bit of bother.
Maybe cat people move and act a bit more like happy cats. More possible, cat people have learned over time simple body language, and even if they don’t realise it, they move or act in a more happy cat manner. Seeing a cat might make more such behaviour likely. Cats training humans as usual.

This.
I’m good with dogs and cats, but that doesn’t mean no animals are initially wary of me. It’s that I know how to indicate I’m non threatening (also: that I am not afraid of them; they won’t approach someone who acts frightened)

I wouldn’t count on that.

Some years ago, I had a visitor who was entirely unused to cats and terrified of them. I also had a large but very shy cat who almost always avoided anyone he didn’t know well.

We were sitting in the kitchen, and Shy Cat came in – and to my astonishment jumped up into Frightened Person’s lap. She froze entirely, except for saying ‘what does he want?!’ in a very shaky voice. He sat there looking entirely comfortable. I said ‘He wants to be patted. Do you want me to move him?’ and she said yes and I reached over and took him off her lap.

I don’t think she took her total lack of injury from the incident as particularly reassuring.

Well they generally won’t.
I guess what I was getting at, is that people who are nervous around cats will do things like jerk their hand away because they are scared they are about to be bitten.
But that jerking away of course makes the cat nervous, and may even put it in fight or flight mode. So you have this cycle of people who are nervous around cats having experiences that make them nervous around cats.

And vice versa – calm behaviour gets rewarded. Although…no-one’s dr dolittle, and sometimes all you can do with a super nervous cat, or one which has “scratch” as the default response to any new stimulus, is to leave it alone for now.
And some cats seem to have neurological issues – my friend had a cat that would occasionally just launch itself at people and be in full-on bite + scratch mode, just out of the blue. Apparently it had had some kind of accident, but my friend had explained in Spanish, and I didn’t quite catch what kind of accident and how it could have had that effect.