You pay taxes into the school system even if you don't have kids, much less have kids not in the school system. So that logic isn't logical. I'm all for home schooling, thinks it's great, but I think part of home schooling mean no school activities. You're in or you're out. If you went to school X you wouldn't be eligible to be in the marching band for school Y, well home is a school X and she wants in Y's band. Seems pretty universally applicable to me, if you don't go to the school in question, regardless of where you do go to school, you cannot be on any of the teams sports or acedemic; no football team, no chear squad, no marching band, no theater group, no chess team. Not for kids that go to a different school in the same system, not for kids that go to a public school in a different system, not for kids that go to private or charter schools, and not for home schooled kids. It's perfectly logical and perfectly fair.
Makes good sense to me.
You say she's half-in/half-out, I say it's the school district.