Why did Cherry and Marcia leave their dates in The Outsiders?

Cherry and Marcia left their dates because they brought alcohol.

Cherry and Marcia are Soc girls.  They do not approve of their boyfriends’ methods.  The boys get drunk too often, and get violent.  Cherry and Marcia explain that they left their dates because of this.

Oh, yeah, we found out why they were without a car. They'd come with their boyfriends, but walked out on them when they found out the boys had brought some booze along. The boys had gotten angry and left. (Ch. 2)

Socs and greasers do not usually hang out together.  There are very specific class distinctions between the two gangs.  They are often fighting, and the Socs have a tendency to jump greasers who are alone and not defended by their gang.  However, the main problem that Cherry has with her boyfriend Bob is his drinking.

Bob comes up to Cherry and tells her that he is only a little drunk.

Cherry looked mad. "A little? You call reeling and passing out in the streets 'a little'? Bob, I told you, I'm never going out with you while you're drinking, and I mean it. Too many things could happen while you're drunk. It's me or the booze." (Ch. 3)

Cherry does not want to get into the car with Bob, but she does because she does not want to cause a fight when the Socs see the girls with greasers.  Pony and Johnny are ready to fight, and she can see that.  Unfortunately, the Socs come back later and find Johnny and Pony in the park.

Later, Randy explains to Pony that Bob's parents were too lenient with him.  They let him get away with anything, and did not get involved even when he came home drunk.  He is a spoiled rich kid.

The incident at the movies snowballs into the disaster that sends Johnny and Pony on the run.  Bob and his friends jump Pony and Johnny in the park, and Johnny kills Bob to prevent him from killing Pony.  Neither of them wanted to kill anyone, even a Soc, but it was self-defense.