In American public schools, if a child doesn't attend, is she shut out from all of its offerings (better explained in OP)

Not sure nowadays, but in Canada back in the dark ages, kids were offered insurance against injury etc. in extracurricular sports (“take this home for your parents to look at”). I’m not sure if it was mandatory, since I never played any, but it was a few dollars for the year. The fine print made for some hilarity - “Oh, I can get $1,000 if I chop off a finger…” And, of course, Canada does not have the fine tradition of litigation that we see in the USA. I don’t remember anything about it in high school, so I assume it was something that faded away, or the school realized it was liable regardless and got its own insurance, or something.

[Moderating]

Whom are you calling stupid?
Wait, no, it doesn’t matter, because you shouldn’t be calling anyone stupid in FQ. Which makes this a Warning for personal insults.

I think PA has this law for extra curriculars like sports and clubs. I don’t know that this applies to say, a Saturday night dance at a school. I could see where it may not. IMO. it’s a lot easier to know which kids are on your soccer team, cheer team, etc than it is to know which kids from which schools (home schools included) are showing up at a dance. I really don’t know.

When you’re selling the tickets, you only sell them to students from your school. Each student either buys one ticket (for just themself) or two (for themself and their date).

When people show up to the dance, everyone has to give a ticket, and everyone has to show a student ID. And I imagine that the chaperones know more or less what the IDs for the most likely schools look like.