To be fair Mrs. (And to a lesser extent Mr.) Don't have an obvious pronunciation from the spelling either. You've just been hearing them said out loud for most of your life.
Apparently it's short for "Mix". I only learned that in this post, which suggests it's far from established - I assumed it was along the lines of "latino/latina -> latinx".
Obligatory "Latine" is the preferred gender neutral term for spanish speakers because it actually follows the gendering rules of the language, rather than english speakers making shit up.
I'm not saying it's difficult to teach or learn, but if you first encounter it in a book are you going to know it's pronounced "mix?" And if you hear is are you going to know it's spelled "Mx?" You can argue difficulty all you want but if you have something that is spelled how it sounds and pronounced how it looks it's still easier and there will be less confusion.
I mean if you see “Mx” and you don’t assume it’s pronounced “mix”, you might have some elementary language difficulties. I understand not being sure, but it is pronounced how it’s spelled.
The better idea is not to make up terminology that only suits you and an exceptionally small minority and then expect everyone else to adopt it.
By all means, define yourself as you like - but don't expect others to immediately recognise that definition without reasonable explanation.
This case has nuance. On the one hand, a teacher in Florida is not allowed to talk about gay people or anything about alternate genders, per state law. On the other, Federal Law states that no one can be fired over matters regarding sex. Federal law overrules any laws states make, hence the ruling in 303 Creative vs Elenis, however the question is what "sex" covers in the Federal domain.
Whatever they like, and other people should be reasonably accommodating to that. Meanwhile, people using rarer honorifics should be accepting that others might find it unusual and sometimes hard to remember.