<p>My son does. He was on the debate team of a neighboring high school (NOT the high school in our school district) last year, and he will join that high school's math team in the fall, after being the sole member of a homeschool "team" in the immediate past school year. In Minnesota, debate is regulated by the State High School League much as interscholastic sports are regulated, while the Minnesota Senior High Mathematics League is an independent organization. Lots of homeschoolers here participate in public school extracurricular activities, including team sports.</p>
<p>In Oregon the law requires public schools to allow homeschoolers to participate in interscholastic extracurricular activities--that is, those that include competition between schools, such as sports, band, debate, etc. My sons both took part in some of these activities, and they also took some classes at the PS, as our district was very accomodating of homeschoolers.</p>
<p>In NJ, local districts make individual decisions about how much they will allow homeschoolers to participate. Most of the NJ homeschoolers I know are happy to stay completely out of the public schools, and don't ask for anything. Part of the reason I think is that there are much better options outside of the public schools here. It's a heavily populated area only miles from New York City, meaning there are hundreds of arts, science, language and sports programs available in the communities. Public school students are actually here, in that they do not have time to participate in all of the outside activities.</p>
<p>My son is a partial home-schooler. Some classes at the school, some elsewhere. He participates in Moot Court and Junior State, was on the ultimate frisbee team, started a club on games of strategy. The Moot Court was superbly run. The judges for the final round were actual state court judges including state supreme court judges.</p>