Therefore, if we were to stick with your logic, public schooled kids shouldn't be able to play music with any other band (or sports team, or whatever) besides the one public school supplies...even if their parents pay for it with their tax money, correct? This is, in essence, what you are telling the homeschooling family.
Yes it is. Enroll the kids there or not. You can't and shouldn't be able to have it both ways. Having it both ways would be most unfair to people like me that have chosen to send kids to private schools. I still pay school taxes. I don't get a thing from my school taxes. However, I wouldn't even think about trying to get my kiddo into the local middle school band because her private school doesn't have a band. My daughter doesn't go to school there. The principal would be fully within his/her rights and correct to tell me my daughter can't play in their band because she doesn't go to school there. It's pretty much a no-brainer.