Obviously there are deal breakers like being right wing or racist or having an unhealthy interest such as sexual activities with small furry animals
but petty? Make up. Sounds silly now I say it but in my mind if I meet a woman wearing a lot of make up I just assume that we won't have much in common. My bad, probably, as I never get to find out.
Or if someone shows interest in celebrities, same again. Or they talk about soap operas.
Oh no! So be just realised I'm the king of petty judgments and destined to live the rest of my life alone

They get a restraining order against me.

Petty: I prefer not to date women with dogs. Cats are ok. And no, I was never bitten by a dog, and I HAVE dated women with dogs. I guess I just don't like the smell, mess, inconvenience of the dog... it's not worth the advantages to me. That said, a child is ok. Go figure!

I have a thing for the sound of a woman's voice. It can be a serious pro or con.

For me it would be smoking (I don't like kissing girls that smell like ashtrays), strong religious views or faith in superstition. I've tried it and it just got incredibly annoying to be put-down by illogical faith arguments.

Petty? A higher voice than mine/a bad laugh (went to a movie with a 6'6" guy, wanted to crawl under the seats when he'd laugh: he sounded like an 8 year old girl. Any attraction disappeared instantly.
Most of the ones people are posting, to me, don't seem petty at all... or maybe I'm just that petty??

Smoking, religion

Smoking

Mainstream tastes.

High fiving in public

Wouldn't really say this is PETTY petty, but I couldn't go out with someone super left- or right-wing. They're too strongly opinionated with certain things and don't listen to reason.

They don't give me their name. That's a pretty good one, I think.

Would annoy my wife.

I won't date a woman because she doesn't have a penis. I know that makes me sexist and shallow, but it is what it is.

Too religious or conservative, those could be definitely deal breakers

If they don't like Tom Petty!

I have MANY.
If they dress like a low class person with slovenly grooming habits.
If they golf or hunt.
If they make a crude sexual remark to me, or about another woman in my presence.
If they own a large dog that they allow the run of the house.
If they own cats.
If they eat junk food, or think of food as the highlight/goal of any event.
If they are flabby or lazy.
If they don't read very much.
If they have never traveled and don't want to.
If they have no curiosity.
If they are (most) ethnicities, because their attraction is often because I'm white.
If they are poor and/or homeless, such as living with their mothers or friends.
If they are Conservative and/or religious, unless they aren't serious about it.

They don't have a job
They are aspiring "whatever" type
They are Republican
They chew too loud
They are obese or too skinny
All the hygiene stuff
They don't read

Someone who's stupid

The pettiest I've been? I stopped chatting to a guy on a dating site because he couldn't phone me until he'd been paid and could top up the credit on his phone. I'm no gold digger, but I expect a partner to pay their way. If they can't afford £10 for mobile credit, then it seems quite likely that I'd end up paying for everything on a holiday or a night out.

I won't date a woman that smokes.

...because I married.

Not sure what you define as petty vs. what I define as petty when it comes to dating. But the fact that they was born a male would throw me.

Bad manners - around me, or others.

I do not date smokers. I am not anti smoking, but hate the taste in their mouth, and the lingering smell in the car, house, and on my clothes. Could be that my ex wife was a smoker too. This pettiness has cost me a chance to start something meaningful more than once