I think that children who are home schooled under the guidelines set up by their local school districts should be allowed to participate in public school sports. Parents of home schooled kids still pay taxes into the school district where they live, and that money helps fund those sports programs. Social interaction through playing sports can be very beneficial to children that are home schooled and they should not be denied that opportunity.
I think it doesn't matter if you are a home schooled kid or not. The only thing that matters is if the kid wants to get exercise, or have fun. Most kids around the world don't like to exercise anyway, so let these kids do what they want to and be healthy.
Many public schools have requirements for their students to be in a sport, they work hard just to even stay in the team. Letting home schooled students join may discourage some students. Their are community sports, or private sports they can join. Home schooled students parents have opted out of the public school system, so why let them join.
There are plenty of private sporting clubs that home school kids can be involved in. Many of them even offer sports classes during the day especially for home school kids. School sports are for kids who attend that school. You wouldn't allow a kid who goes to another school to play sport for a particular school
So why allow a home school kids?