I'm reading she essentially agreed to a contract in the form of the "team rules" and then violated those rules for which she was held accountable. This isn't a free speech issue, it is a contractual issue.
1: She could not legally sign that contract
2: The cheerleading team is ultimately an extension of the government (as it is part of a government institution).
By literal means, the state is punishing someone for what is ultimately private, off-campus speech. A lawyer with goals in life would see that as a case worth fighting.