I wouldn't want my 6 year old doing that cheer, either, honestly.
I wouldn't be surprised if some of the "competition cheer" teams did cheers that I thought were beyond-the-years of the little participants, and I would choose not to enroll my child in that. However, it doesn't sound like this is a competition team. It's a community flag football cheer team. I would expect that to be quite age-appropriate. (Kind of like I think there's a difference in what's expected from "competition" dance teams and recreational dance recitals. I would expect the recreational classes to stay middle-of-the-road.)
I personally think they should stick with cheers that don't talk about 6 year olds in "too tight" skirts and booty shaking. However, if they said "We're not changing the cheer, but we'll offer you a refund if you want to withdraw, or you stay and do the cheer." then I guess I'd think that's fair. But kicking the girl off without any warning seems ridiculous.