While the other parents are perfectly within their rights to remove the child, you have the circumstances wrong.
This girl's parents complained about the cheer. She did not author it.
For the complaint, the other parents booted the girl. Within their rights, but as you say, it is a reflection on their parenting.
OOPS!
Maybe I ought to wear the cheaters?
So, other than her parents complaining (about her having to do the cheer, I suppose) the kid was innocent? I owe her, her parents, and APS readers an apology, which is hereby respectfully tendered.
Now - as for those within the organization who approved of the cheer - take everything I sad before about needing maturity and something resembling common sense and apply it to yourself.
Does anybody remember the flap stirred up by the little girls dancing to "All the Single Ladies"? (No, I'm not going to give you pervs a link to it!) Amazing that another storm cloud is not raising over this.
stay safe.