That goes double when we are talking about public employees whose conduct is directly the function of law.
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 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.
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."
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
Pornography is pornography and pedophiles are pedophiles, but please, feel free to make your case for this.
Do you consider a curriculum to be a restriction on freedom of speech? I ask as a genuine question - being from the UK the norm for me is having a national curriculum and standard testing (albeit it executed by private-but-certified exam boards). It seems like common sense to me that obviously teachers have restrictions on what they can say in a classroom. Any employee does within their workplace and job duties, but teaching is one profession where I'd clearly expect a much higher level of restriction (along with the police, who represent the state, and doctors, who have duties of professionalism and to give medical advice only in line with the regulator, and various other regulated roles)
Yes. Restrictions on what teachers are allowed to teach are restrictions on freedom of speech. Restrictions on non-sexual drag performances are restrictions of freedom of speech. Bans on calling for boycotts of Israeli goods and services are restrictions of the freedom of speech.