Home Schoolers Denied Extracurricular Activities

In New York, public schools are prohibited from allowing home schooled children to participate in interscholastic sports but each district can set it's own policy on extracurricular activities. In a survey, 34 CNY schools deny these children participation, one of them being our school district, while 4 districts allow it. One had no policy and 7 didn't respond.

Ok I don't get it. Home schoolers pay school taxes so why can't they participate in plays and sports and the band? My kids go the public school and I have friends that home school. I wouldn't want to home school my kids simply because I feel the social interaction on a daily basis and learning to get along with people you hate is just life. I feel it's best for my kids to learn these skills early and they can come home to their parents at the end of the day and discuss the trials and tribulations of relationships, both with their peers and their teachers. But opinions aside, I can't see the harm in allowing these home schoolers to be in the play or the band or on the various sports teams. We could especially use their help because we are a tiny school. So what am I missing? What are our school districts gaining and what are they losing?