If one is opposed to public school to the extent that you remove your children from the system, why would you let your child represent the school you oppose by being on their football team?
Just because someone homeschools, it doesn’t mean they are against public school. It may just mean that it is the best educational choice for their child. I know families with one child in public, one child in private and a couple that are homeschooled and many variations on that theme.