Sports or Extra Curricular Activities come with additional responsibilities than simply attending school. When you participate in these activities you become a representative of the school. In a simple example this is why most sports teams ( used to ) wear ties and or slacks on game day.
The community and the school views you as an extension of the school's pride and standards. You sign a contract to this affect when you join the activity.
Cheerleading has a unique set of requirements beyond other programs. In some schools the student body votes for the cheer squad, in others the ASB council does. Sometimes they are members of the ASB council. In some schools that are actually considered a sport ( inside joke for other who have been involved in cheer, and yes it is one of if not the toughest sport ).
This makes the contract a Cheerleader signs a bit different than other activities. The contracts do become a bit vague. However, sending out an instagram as the one in this instance would certainly fail the criteria for most cheer contracts.
Activities outside of school typically prohibited by most activity contracts include drinking, attending parties where illegal activities are occurring, being arrested, disparaging your team or opponent, bullying any member of the student body, etc.
My two cents, the severity of the punishment is the problem. I believe the penalty outweighed the violation. A single game suspension and an apology would have been a better teachable response. Instead they created a crisis where one did not exist.