Why can Cherry and Ponyboy not socialize at school or other places?

The Socials, or Socs, are the wealthier kids while the Greasers are the kids from the opposite side of town with less money and fewer opportunities. Ponyboy explains how the girls from the Socs' side "looked at us like we were dirt" in much the same way the Social boys driving in their nice cars look at Greasers.
At a drive-in movie, Ponyboy and Johnny end up sitting with two girls from the Soc side. One of the girls, Cherry, seems to like Ponyboy, and they end up having a long conversation. When they stand in line together to get popcorn, Ponyboy notices the stares they are receiving since it is rare to see a "kid grease and a Socy cheerleader" together.
During their conversation, Ponyboy and Cherry agree that not all Socs are the same in much the same way that not all Greasers are the same. However, Cherry explains to Ponyboy, "if I see you in the hall at school or someplace and don't say hi, well, it's not personal or anything." The reason she can't be seen talking to Ponyboy at school is because of the unwritten social rules of class. Greasers are seen as being beneath the Socs, and to be seen hanging out with one is frowned upon by the other Socs. Cherry knows this is wrong, as does Ponyboy, but the unwritten rules are difficult to change.