It is not a right to play a sport it is a privilege at least according to the former public high school my daughter attended. It is stated that way in their handbook - it clearly states that playing a sport is a privilege and not a right.
You have to be very careful with this, because defining sports as a "privilege" allows for discrimination of any type.
How would you stop a school from saying that children with same sex parents (for example) couldn't be on the school team?
Because there are also policies in place in regard to discrimination within the student handbook that addressing all that stuff - sexual orientation, race, religion, etc.
This is why these damn handbooks are so large (they have to encompass so many different things and why no one reads them even though you must sign them as a student and parent.
Interestingly though - there is nothing about inappropriate behavior off school grounds and/or outside of school functions - other than legal ones ...
My daughter's private school she attends now, though does include behavior outside of school including summers and vacations (clearly stated in their handbook). The expectation is that they are of a particular character...which you get as you interview to get accepted at her school.
Also interestingly enough - her private school is so much more understanding and bends their rules significantly more than the public - I used to warn her that she could get kicked out of her school for certain behaviors - she honestly loves this school and wanted to leave public for this school so it is a good threat - but as I found out - they have a handbook but they really do not follow it - with the size school they know all the families and students so well they can "customize" things that tend to work better to get the desired results.