The restrictions on teachers you speak of are in their functions as employees of the state while performing their duties on the job on the employer's time. Employers setting limits on the conduct of employees on the job is generally not a freedom of speech, or first amendment issue.
That goes double when we are talking about public employees whose conduct is directly the function of law.
> Employers setting limits on the conduct of employees on the job is generally not a freedom of speech, or first amendment issue.
In other words: you're allowed to restrict the speech of other people as long as you own private property. Turns out that freedom of speech in a liberal "democracy" is not all it's cracked up to be.
You skipped the rather pertinent bit where these restrictions apply only to people who chose of their own volition to take them on.
You are, of course, free to not take on the burden of employment from a particular organization if you find their demands on your conduct while they are compensating you for your time to be unacceptable.
This relationship is purely transactional. And, sorry, the idea that this is actually a bona fide problem is facile.
That line of reasoning would make sense if the have-nots in a liberal society didn't need to work just to survive. But that is not the case, is it?
Liberal society loves to characterise itself as a rigid, well-structured system in which individuals choose to make idealised rational decisions to work towards their own interests. As opposed to emotional reasoning, which is conveniently implied to be the diametrical opposite of rational thought. And I call it "convenient" because as a result can easily paint protests and strikes, as "irrational" and "despicable" actions perpetrated by "unreasonable" individuals.
However, as soon as one considers the fact that the disparity of power between people with private property and people without makes it so that the people without private property cannot afford to make decisions on a "rational vacuum". We quickly find ourselves reverting back to "what are you going to do about it? You don't work, you don't eat."
Indeed, allowing employers to coerce the speech of employees by punishing them for actions outside of the reasonable scope of employment is very worrying. Unfortunately, a good deal of the modern "left" supports it when they dislike the person. Much of the right does too, which I have equal disdain for, but I will at least acknowledge it can be logically consistent with some right-wing philosophies (on the more ancap end). Whereas it's a bit strange to see "socialists" saying "but they're a private company!"
However speech in the classroom is within the scope of your job duties. So my employer should not be able to fire me for wearing a Trump or Biden sticker off the clock, but it is fair to prohibit me from wearing it whilst on the job, and to sanction me if I'm proselytizing to customers during my duties
That goes double when we are talking about public employees whose conduct is directly the function of law.