I know several homeschooled students who played varsity sports for their local high school (the one that they would have been attending). I'm not sure about the universality of that, but that's an option for at least some people.

I think it's patchwork & has changed over time. When I was at high school one of my friends who was homeschooled competed with me on our academic team. His older (and far more athletically gifted brother ;-)) lettered in several varsity sports. But now that state's athletic association explicitly says no to homeschool students.