Are you of school age? If not, then your ability to walk in is immaterial.
Home school families most often choose the home school approach due to academics. Time after time we see open events that accept all students from an age group won by home schoolers. Spelling bees are a common example.
One of the sticks used to beat home schoolers into sending their kids to the school is sports and other extracurricular activities. Any student in the district of a certain age is eligible to play or participate, unless their parents choose to sacrifice (while still paying the taxes that would send their kid to the school) by home schooling - again, usually for academics.
The state universities are immaterial, as well. In order to matriculate one has to apply, be accepted, and pay tuition over and above the tax based support. With local schools, there is no such requirement to pay extra.
“Any student in the district of a certain age is eligible to play or participate”
Not if they go do a different public school.
Or a private school.
Or have dropped out.
Or have bad grades or poor attendance.
Or are not students at the school.