> This is a great test case. <
It sure is. Let’s say you’re a car salesman, working for Ford. And Ford demands that you sign a paper promising to buy only Ford products. You refuse. So Ford fires you.
Is that legal? I think so. The First Amendment only protects free speech from government suppression. It does not protect free speech in general.
But here we have not a private company, but a government school. So yes, this will be an interesting case.
If they law said she could not promote a boycott while at work, she would have no case.
But saying she would not engage in a boycott on or off the job is far over the line, and very likely unconstitutional.