The school claim it is about reputational damage not about her relationship with students. So that isn't the issue, making it so is witch-hunting. The bakers refused to bake a cake for a gay event, so that is not the same either.
It's not the same, but it throws up similar conflicting ideas about rights.
The only direct quote in the article about why she was sacked is the one I gave, which is about respect and tolerance, which very much concerns her pastoral relationship with students.
As to the reputation of the school, would you, as a parent, choose a school for your child which, despite complaints, condones a staff member posting that respect, tolerance and understanding amounts to brainwashing? Or would you feel that that's liable to lead to an environment where there's no pastoral concern about, or possibly active endorsement of, those who tell their peers that god doesn't approve of their sexuality or preferred gender? The reputation and atmosphere of the whole school, and of the staff and parents who are involved with it, can be affected by a staff member campaigning in the way she was, potentially to the point that one set of parents shun it and another set actively seek it out. The school management and the rest of the staff may not think that's such a great idea. Reputation matters.
Of course, her job is important. I'd ordinarily suggest she talks to the appropriate union, but they're quoted as being "
in favour of a motion to lobby government to strengthen RSE guidance and make teaching about LGBT relationships compulsory at all stages of the curriculum." She, meanwhile, want to stop books about inclusivity being shown to children.