MN law allows homeschooled children the ability to participate in all extracurriculars, music, and PE. It also allows school districts to provide shared time programs for other academics, but shared time programs are not required.
My kids are in 2nd and K, and they are attending our public school for one class period every day. They go for the specials rotation - art, music, PE. Our elementary school is wonderful, and my kids will be participating in school parties, fieldtrips, and other special events too. We are the only young homeschooling family in our TinyTown, so my kids' friends have to be public schooled kids.