On one hand, everyone’s entitled to an opinion and the right to free speech.
On the other hand, once you are an employee, you can be construed as an agent of your employer, and subject to their rules.
Because teachers fulfill an important growth and formulation role in the development of young minds, I firmly believe that their conduct, both in and outside of the classroom, comes under the heading of moral turpitude.
This is a common clause in many entertainment and high profile career contracts (e.g., as in endorsement deals for products by a celebrity). I believe that this also flows into teaching, even if solely by inference. The school board did well in firing her with cause. Taint that part of her resume, at least.