Galaxy
It doesn't really matter what you suspect growstuff. I hope they get some good advice. As I say the police have got this wrong quite a lot previously, no idea whether that is the case in this incident. Organisations are receiving very hefty fines for getting it wrong on freedom of speech, it will keep happening until it dawns on organisations that the cost for errors in regard to control of speech is very high.
I know what I've read Galaxy. It's absolutely clear this is not primarily about free speech. They weren't arrested for what they said, but for harassment. The man has a public role and works in the media, so is good at self-publicising. He's a former governor at the school and this sounds like a personal attack against the other governors. They had already been visited by the police and banned from being on the school premises and had been asked to take their child away from the school. Schools don't act like that unless something very serious has happened.
Something similar happened years ago at a school where I was working. A parent was disgruntled about something and repeatedly came into school and shouted at people. Eventually, he was banned from the premises, so started bad-mouthing a number of named individuals on social media, so he was issued with a Cease and Desist Order, which he ignored. The school had no alternative but to call in the police, who took him in for questioning. In this case, he was actually charged with threatening behaviour. The school, of course, couldn't defend itself in public until after the hearing and it the whole business caused a great deal of stress to pupils, parents and staff.
More close to home, somebody I know very well is currently being attacked on social media for fabrication of evidence in his books and "owning" a company which has made hundreds of thousands of pounds from the fabricated evidence. I know for a fact it isn't true. When challenged, the attacker claims she has the right to free speech and can say what she wants. She has also targeted a few other people and there is a danger their reputation will be affected. She hides behind social media, but her posts are gaining an audience. I'm not going to write much more because we're closing in on her and when we do, there will be legal action. People do not have the right to say what they want in public without dealing with the repercussions.