The race and ethnicity might be on the school district’s records, and the high school may not be able to change them.
The school and the district do not care what you put on the forms. When we moved to Florida I got a stack of papers to fill out for my kids. First question was mother’s name (easy) but then asked relationship. What? Choices were Natural mother, step mother, foster mother, or legal guardian. None of those were applicable. She is my child through adoption. Didn’t fill it out, never filled it out all the other years either. No one ever asked, they always gave me information about her.
Why ask if you don’t care what the answer is?
I also refused to give them (or the many dentist who asked) SSNs. That was also a question on all forms for my kid to play hockey. In these hockey files are also a copy of the birth certificate and a lot of other info, which are kept in an unlocked file cabinet, are given to the ‘team moms’ in binders to cart to tournaments to prove age. Very secure. NOT.