Some teachers (and other groups, like pro athletes) have a “morals clause” in their contracts, which have been used to try to police behavior of teachers on their off-time. They are legal, but potentially difficult to enforce. Here’s some info:
https://www.findlaw.com/legalblogs/law-and-life/what-is-a-morality-clause-is-it-legal/
I wouldn’t be surprised to learn that they’re counting on teachers who commit crimethought* to not have the time, resources, or inclination to fight it, with or without union or ACLU support. After all, the Superintendent knows how little they’re paid.
*Granted, it’s already illegal to directly threaten the POTUS, so part of this is grandstanding B.S., but even then, my understanding is that you’re just as likely to get a polite-but-firm talking to from the Secret Service as you are to get arrested, depending on your choice of words. I remember another blogger (wish I remembered enough to find the link, but it was many years ago) who shared a story of being reported to the Secret Service for a comment that somebody construed as a threat to Dubya. He said they were very professional and there were ultimately no long-term consequences for him (except probably being on a watch list), but he didn’t recommend the experience.