School - I want to do cheer team but my parents aren't supporting me. I am paying for all my stuff?

It seems difficult to understand what their problem is, given that they aren't being asked to support your decision financially or with their time. All I can imagine is some moral issue but if they had an issue, hopefully they'd be mature enough to discuss it with you as opposed to leaving you in the dark like this.

I know this is going to sound like a very obvious answer but have you asked them why they won't sign the papers?

I think they're just protecting you. They know better. I think they don't want you to face temptation and so much fame.