Specifically in schools, this is problematic because it makes children who do not celebrate christmas feel left out. Adults should be able to handle it, children not so much.
> You can't say you understand homosexuality to be a disorder.
This is not an opinion related to your job, so you should definitely keep it to yourself while on the job. While some people will definitely throw a fit about it if you make the opinion known outside of your job(especially regarding teachers) I agree that this is bad and shouldn't be done.
> You can't call a man "he" if he identifies as a "she".
This is just simple respect. If someone asks you to call them something, you call them what they asked. Even if you think it is wrong/ridiculous. It doesn't hurt you any.
In the context of trans people we're not talking about "hurt feelings". We're talking about murder, sexual violence, severe assault, and increased risk of suicide.
If you are rude or disrespectful to people at your job then you are negatively effecting your job performance and you will be fired due to that. This is anywhere. I haven't heard anyone (though there is probably someone out there, there always is) recommend jailing or otherwise punishing anyone beyond losing their job.
"You can't say Merry Christmas."
First off... yes you can. However, Why would you assume a large group of people in a public setting outside of a Christian context would all want to be wished a Merry Christmas...seems unlikely to me.
"You can't say you understand homosexuality to be a disorder."
Again.. you can say that, However you would be factually incorrect. Mental disorders are "disorders" because of the negative impacts caused in the sufferer's life.. What has been shown to be the negative impacts of homosexuality?
"You can't call a man "he" if he identifies as a "she"."
You can call anyone anything you like... what you don't have control over is how they feel in reaction. Assuming you identify as a man.. how would you receive someone that always referred to you as a female, and I mean always not just as a one-off joke type thing. I'm going to take a guess that you would feel worse than "censored".
Basically, imagine having Dr. Cox calling you Shirley every single day, even though you hate being called girl's names. A lot of it boils down to 'Don't be a dick'.