Can parents exclude their children from any class (in a public school) they don’t agree with? I know parents can exclude their children from sex-ed classes. What about Health classes in general? School assemblies, DARE programs, Standerdized tests, Science classes, physical education classes, etc.
Not around here.
Health classes in general, standardized tests and even a lot of assemblies are required parts of the curriculum.
Accommodations are usually possible. If a parent objects to a particular book in the English curriculum, an alternate book can be assigned. If a student is physically unable to take a Physical Education class, a Health course may be substituted. I know our school district at least considered offering a standard sex ed course with an “abstinence-based” alternative course.
DARE assemblies were optional. Students who didn’t have permission went to study hall. But if a student didn’t take the state standardized tests, there was hell to pay.
Parents can exclude their kids from the whole school, if they wish. It’s often called “Homeschooling”. The parent has to document that homeschooling is, in fact, taking place, but otherwise they can do this without violating compulsory attendance laws.
As far as excluding them from individual classes, that’s a bit more problematic. Remember, at the end of the course of study, the student wishes for the school to confer a diploma. The only way that is going to happen is if the student satisfies the requirements for that diploma. Therefore, opting out of English class because it conflicts with your relgious beliefs can cause you problems if you are wishing to get the diploma.
You cited sex-ed as a class from which a student may be excused. That isn’t exactly true. Sexual Education (in junior high and high school) is usually a program presented as part of another class. Rarely is it a class in itself (though the kids might find the lab section fun! 
). Therefore, the student is simply excused from a particilar program which often isn’t even graded.
I am a band teacher in Texas. At this time of year, I will sometimes have Jahova’s Witnessess who ask to be excluded from preparing Christmas music. I can change the requirements for them without fundamentally altering the course. This is not a problem.
The best way to handle this problem is to visit with the teacher or administrator responsible for the program in question. Don’t threaten, just talk. Is there something in your school that you object to?
As a pratical matter, generally yes, if the parent is selective in the request and pitches a big enough fit. US public schools are increasingly sensitive to anything that might create a national news PR flap.