This is a tough one. Sure, the nice thing to do is let her on the team. It's not her fault that she was born this way and she certainly has more drive and determination that most people in her condition. The storybook ending would be to let her on the team and have her cheer from her wheelchair, happy as can be that she "can do it".
Unfortunately, this coin has two sides. The other being the sad truth that she can't do it. Having no arms and no legs would restrict her ability to do much more than participate in the chants. She couldn't take part in anything else really. No hand springs, no coordinated dance routines, no jumping, flipping, etc. It's terrible that she was born this way, but let's be honest, I'm sure this team cut or turned down at least one other girl who was better suited for the requirements.
Whatever is decided, nobody can say they didn't have a tough choice on their hands. I believe both options could very well be the right choice. I don't feel there is a right or wrong answer here. I think the squad should not be legally required to include people who are incapable of participating at a normal level. I also think that if they choose to incude her anyway, they would get somebody who will really show them a thing or two about what it really means to be excited and optimistic no matter what is thrown your way. If a girl with no arms and no legs is doing all she can to cheer on the sidelines, you'd think players with both arms AND legs would be inspired on more than just the playing field.
I don't think she should be allowed on the team, but I would like to see them invite her anyway. In the end, it won't hurt anybody to have her there, and it will probably do a lot more positive for those around her than they realize. This is the type of emotional journey that you see made into movies, depending on how the school board rules of course.