I have no problems firing a person for cause. But you have to make the case, not just assume that because a person says something, it means they would also act in a certain way.
I’ve certainly said things occasionally that, if used as the sole judge of my character, would find me quite lacking. I take great care not to write things that would do so, as I like having a job.
I can imagine several things said regularly on this site, that if they were put on facebook by a teacher, might get a similar reaction to that which we have now — and in some cases, I am pretty sure those people would make fine educators, even with their biases and prejudices.
I’m not trying to judge this particular case, which is why I started with the general comment that it makes me nervous whenever I see people losing their jobs for expressing an opinion.