“Title III, which this rule addresses, prohibits discrimination on the basis of disability in the activities of places of public accommodation (businesses that are generally open to the public and that fall into one of 12 categories listed in the ADA, such as restaurants, movie theaters, schools, day care facilities, recreation facilities, and doctors’ offices) and requires newly constructed or altered places of public accommodation—as well as commercial facilities (privately owned, nonresidential facilities such as factories, “

https://www.ada.gov/law-and-regs/title-iii-regulations/

So yes they’re violating the ADA. A private school is a business and a school. All activities are required to be reasonably accessible. Since diabetes and epilepsy require no accessibility provisions for the activities you’re talking about, they’re covered by default.

State or federal funding doesn’t play into this requirement although ADA violations are a reason to hold back such funding.

The school is engaging in discrimination.