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

Let’s say that Jenny lives comfortably within the boundaries of where the students at Prototypical Public High School (PPHS) gets its students, so there’s no ambiguity about what school she would attend if her parents enrolled her in public school. Her parents home-school her because reasons, but they feel like they’re not qualified to teach her Chemistry, so they want her to go to PPHS’ Chemistry class. Is that a thing that can be done in the US public school system, or is it kind of an all-or-nothing sort of situation? Could she join their soccer team? Get counseling from its counselors?

Let’s say that Beth is also eligible to attend PPHS, but her parents instead enroll her in Uptight Presbyterian Private School (UPPS) because reasons. UPPS doesn’t have dances, being uptight, and she wants to go to PPHS’ homecoming dance. Can she do that?

I will concede that this is going to vary greatly by state and school district, but if you can provide anecdotes about your own public school system’s rules that’s fine.

AIUI, no: in most public schools, you can’t pick and choose which class your kid attends, other than electives, which, if enrolled, you can choose. You’re either enrolled in public school, or you’re not. However, there are lots of home-school co-ops and online home-school classes you can take advantage of for a particular subject.

About two-thirds of the 50 states have so-called “Tim Tebow laws,” which generally give home-schooled students in those states the right to join extra-curricular activities at public schools, including sports teams. The laws are named for former NFL quarterback Tim Tebow, who himself was home-schooled but played football for a public high school team. Such laws don’t generally extend to academic classes, but would extend to academic-oriented extracurriculars like mathletes.

I looked this up via AI and got the answer I expected: that it varies greatly from system to system. AI also mentioned that Florida has a law that allows home-schooled kids to participate in public school sports. The law was named for Tim Tebow who, if you don’t know, was home-schooled by his uptight religious parents but was a star on the football field and was allowed to play for his public school’s team.

ETA: Severely ninja’d by bibliophage.

I’m pretty sure at my kid’s public high school (in a state that does not have a Tim Tebow law as described above) you can’t just decide that you want to take chemistry or be on the soccer team if you’re not otherwise enrolled. (…On the other hand, you can enroll and get yourself into a situation where eventually you’re taking almost all of your classes from the nearby community college, so it starts looking sort of similar from the other end.)

What is allowed: the school e.g. gives the AP exams and other exams like the American Mathematical Competitions, and they do allow kids who are homeschooled, or whose schools don’t do that particular exam, or whatever, to take them alongside that particular school’s kids. (ETA: I think the difference is that there are limited spots and resources for the classes and the sports teams, but in practice not enough additional people will want to take the AMC that they will run out of spots in any meaningful way.)

My kid doesn’t do dances but I think you need a student ID at that particular school to buy a ticket. Though I’d think if you have a date who attends the school it would be fine to go.

Back in the 1980s my particular Prototypical Public High School was quite diligent about whom they did and didn’t let into dances, and without at ticket and a date from my school, if you didn’t have a Southeast HS student ID you weren’t getting in. I imagine it might have had to do with gang rivalries and keeping kids from rival gangs at other schools out of ours.

This was close to 30 years ago, but adding a data point…

I technically didn’t go to senior prom with my girlfriend (now wife). I officially attended with her friend, who had graduated early with a GED. My girlfriend officially went with some guy who had been kicked out of our school and sent to the local alternative HS, but just so happened to be dating the friend I was bringing to prom.

In other words, non-students just have to jump through the right hoops.

Also, as far as I know, AP exams are open to any student wishing to take them, not just those in the corresponding AP class.

I think the reason actually is that not every high school administers those tests so there are always people taking those tests at a different high school.

As far as homeschooled students just taking chemistry it wouldn’t generally be allowed in my district. Home school students also do not have access to most school based programs including sports and extracurricular activities.

The reason I say it wouldn’t generally be allowed is because it’s possible for a senior in high school to need only one or two classes to graduate and that’s all they would be required to take. So if a home-schooled student only needed chemistry to graduate, I can’t see how they could refuse to allow the enrollment when they would allow it for a kid who had been enrolled in public school since kindergarten.

Because the student is going to get a diploma that says “Prototypical Public High School” on it. You can’t get a diploma by just taking one class at PPHS. Follow the curriculum provided by your homeschool cooperative or whatever.

When a homeschooled student arrives at a public school – say when they are around middle school or high school aged – the public school gets to decide what grade in which to enroll the student. They will usually base that upon some sort of academic evaluation, as well as age. The student may not be placed into the grade he/she desires.

Of course not - but it’s still at least theoretically posssible that the student will be evaluated and it’s decided that only chemistry is needed. Just like the student who attended Prototypical Public High School Three Counties Away in the same state for three years who only needs chemistry senior year will get that PPHS diploma.

Yeah, but high schools, at least in Texas, don’t have part-time students (mostly). So, that transfer student is going to need to pick up a full schedule, even if they don’t apply directly to graduation. Even that kid from three counties away is going to need to fill out his/her schedule. (And the kid from three counties away still followed mostly the same curriculum as PPHS, so his/her diploma is justified. That’s a bit different from my studying for four years at Pudunk University and then picking up one class at Harvard to get my Harvard degree.)

I’m sure, but I don’t live in Texas and my district apparently has different rules than yours. And the requirements for homeschooled students in terms of how many years of English, SS , math, science etc are the same for home-schooled students as those attending a high school.

One, most home-schoolers don’t teach the classes themselves anymore (though there are some hardcore ones out there), but use online resources/books/etc.

As a data point for the extracurriculars: my niece had a teammate that was homeschooled, but lived within the district boundaries, so he was allowed to play football on a school team.

Others have covered the extracurriculars pretty well, so I’ll say more about dances: At my school, to attend a dance, you have to either, A, be a student at the school, or B, you have to be both there as the date of a student at the school, and you have to have a current student ID from some other area high school. I think there might also be some sort of “permission slip” from the other school, but that’s handled behind the scenes (and so far, I haven’t been the person behind the scenes handling it).

If someone really wanted to bring a homeschooled student as their date, and they went to the administration about it, they might be persuaded to bend the rules, but I don’t think it would work with the current procedures.

One other point possibly relevant to the OP: If a student is enrolled in a school, and is also in some extracurricular, it’s typically school policy that if the student is absent from school on a particular day, they aren’t allowed to attend any extracurriculars on that day, either.

Don’t know about private schools but public schools may have a real liability concern.

Would insurance even cover someone not enrolled?

Any way it cuts down on ringers getting slipped in.

In Missouri it used to be up to the individual school district to allow home school students to participate provided that the home school student took at least two classes from the public school. That changed this year, and now all school districts must allow home school students with no requirement that student be enrolled in any public school class.

Funny, no home school student ever seems to want to try out for the school play or newspaper.

Follow the money, stupid.

The major reason public schools here in Minnesota are hesitant about this is that each student enrolled in the public school system brings with them $7,705 in state money for that school district. This per-pupil aid is most of the funding for public school districts (about 2/3rds of their budget).

So if the kid is enrolled in a non-public school, or home schooled, then the public school does NOT get that per-pupil funding – so why should the school spend money teaching that kid in a chemistry class or coaching them in a sport? That would be taking money away from their enrolled students to benefit these ‘freeloader’ kids. Not likely to be supported by the local parents in that district – who are also the voters of that district school board!

My state does have a Tim Tebow law, but I don’t know what exactly it covers. In my district, home schooled students ARE allowed to participate in extra curricular activities and enroll part time in public school.

From a PDF linked from the page at the bottom:

Students in home‐based educational programs may participate in any extracurricular or interscholastic activity in which the district is involved so long as the student maintains eligibility

Students in a home‐based educational program may apply for enrollment in classes offered by District schools while they are in home instruction

So yes, in my district a student could attend home school for some classes and public school for other classes.

Yeah, it’s all too local to make a definitive statement. My state does not have a Tim Tebow law, so you’re either in or you’re out. My co-worker who home-schooled three kids through at least middle-school (via an organized parental network) had three different experiences. Eldest tried (a very good) public High School, didn’t care for it, returned to the homeschooling network. Middle child was very social, so attended HS for that reason. Youngest attended HS primarily so they could play HS football. All of them later went off to college.

My sister homeschooled her two kids and she used a lot of homeschooling groups and online classes. There are a lot of materials available as well.

She homeschooled my niece all the way through but my nephew wanted more social interaction so he went to a public high school.