Your thinking has been poisoned by SJW rhetoric.

I don't remember Ajax raping anyone. Mercedes Ruhl was out there as bait but all that really went on was some trash talk and nasty flirting. What was the charge?

I wouldn't say there weren't any gays around.. there was Rembrandt.

going beep

I think people appreciate that he's vocal with where he stands, there's no trickery or lies - he doesn't like you he'll straight out tell you. That and despite the issues he has with the rest of his gang during the movie, he has their backs. There might also be some sympathy for him, he didn't run out on his fell Warriors at all but they gave up on him when he needed them. Now it's debatable whether they should've rescued him or not but that's what some may feel.
If you ever get to read the original book which the movie is loosely based on, the character of Lunkface is Ajax. But you read the book really all the characters there are worse than Ajax from the film I think. So at least in translation they made him a much more likeable character

I like him because I have friends like him.

I think that answer makes the most sense to me of anyone's. Someone who is a brutal fighter and a bit "nuts" is scarier than someone who is simply a brutal fighter.

The answer is simple. If you could pick one soldier to help defend your turf

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"Why do people like Ajax"
It's a great cleaner.

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stabbed in the back by The Warriors
Nobody stabbed Ajax in the back. Ajax abandoned his brothers when he decided his dick was more important than sticking with his gang.

This is what happened to Ajax after he got out of prison for attempted rape etc, and being stabbed in the back by The Warriors: https://www.youtube.com/watch?v=FWEQfN39sTo

They don't. They just don't want to get called a "wimp" or a beep
But evidently getting "a nightstick shoved halfway up his a**" was a cathartic experience for him, because this was Ajax a year later:
.
"In a time of universal deceit,
telling the truth is a revolutionary act."
George Orwell

Nawmaybe on the surface, but to a real Warriors fan, it's much deeper than that. He's reckless, a wild-card for sure, but is loyal to the group and will back up his fellow gang member. It takes all kinds. I love him for his kick-ass personality, takes no sh, and doesn't listen to anybodyrisky to take him along, but he must be able to fight like fKK or else why would Cleon want him there as a representative?
"You can just stand there and let him kick your ass!" Karate Kid III

I think just the line "I'll shove that bat up your ass and turn you into a Popsicle" made him a fan favourite nevermind his fighting skills and loyalty

romwfan123, I sooo understand and agree with all you said. This is one of my go-tos. It'll get old only when I have to buy a new one to replace the worn out one.
Ignorance isn't bliss. Ignorance is laziness. So stop being so lazy!

Thanks for the thoughtful reply. Makes sense.
I guess I have a hard time valuing rebelliousness and loyalty without validating context. And maybe I even have a bias of assuming they represent negative traits, until proven otherwise. So much evil originated as rebellion. So many horrible acts committed out of loyalty to evil causes and people. (I do very much value those qualities, they can represent the best of us, and move us forward as a society, but am wary of them since they are so easily used for bad ends.)
So with Ajax I just don't find the context I need to feel like his qualities are positive. I mean, maybe if The Warriors were some charitable gang that had street fights but also pawned property they stole to raise money for hospitalized kids on Coney Island, then maybe I could find something redeeming about him.
Beyond that, Ajax reminds me a bit of a person I once knew He was an "eco-warrior", who would get into violent confrontations when at protests at nuclear power stations, would go to participate in riots against G8 (or whatever the number is now) meetings. It became almost instantly clear after knowing him a little while that he had no moral convictions, his depth of desire to help the planet was paper thin, he was just a guy that liked to hurt people, damage property, use drugs, what his causes were didn't really matter, they were just the fuel he used to elevate his rage and the excuse that made him feel it was justified. But he was sure it was all real and valid. Ajax seemed a bit the same way to me, lots of destructive energy just looking for an outlet, a target, whether it was in the gang, an enemy outside the gang, a woman, didn't really matter. His rebelliousness didn't seem to have any real purpose, it just gave him the impetus to be aggressive. His loyalty also didn't seem to have any real substance (his initial contest for control of The Warriors), it just gave him a "moral" justification for fighting.
But, I don't know, that's my impression.

Glad you hooked on to this great film, it's a blast. Been watching for 30 years now, and see it 2-3 times yearly, and it never freaking gets old. Characters, direction, music, it's the real deal. So full of flavor. Nothing better on a Friday night late, throwing in The Warriors to settle you down for the night.
Regarding Ajax, he's a complex character with a lot of upside. For instance, he can fight like a mother, is straight up bold, takes no beep from anybody, and is challenging for leadership. True true, he doesn't "play well with others" and "doesn't follow directions well", but that's what makes him so appealing. Love that he saved Cowboy, and stood up for the gang on many occasions. Yes, of course, he was a lone-wolf, but that's who he was. Remember, he WAS picked by Cleon to be one of the top 9 in the gang, an honor that was bestowed upon him. Someone liked himhe was just hot-tempered and antsy. As for his raping women, no, nobody's down with that, he's rough, maybe too rough on women. Has to tone that down for sure, agree thereit does make him unlikable, which I can see.
As for why people like himhe does his own thing..he's rebellious and doesn't listen to anyone..something appealing about thatand he can throw those thangs!!
"You can just stand there and let him kick your ass!" Karate Kid III

Because Ajax is a bad a$$, funny and deep down loyal.