“Basically, you’re supporting the notion that it’s a-o-k for the school to make any sort of decree at all, no matter how ridiculous, or blatantly prejudicial, and the school gets a pass.”
And so would YOU, if you kick someone out of your HOUSE for ANY reason, and yet you need no contract at all!
You chose a really bad example. My house is not a public accommodation in any sense of the phrase, whereas a school that accepts public funding very well may be.