"The public" really means "the media and political establishment" here. The late Queen wasn't a threat, William and Kate do not appear to be (as opposed to Harry and Meghan) but Charles speaks his mind and worse still is often proved right.
He does seem a complex person but he has been years ahead of society on loads of issues - aesthetics, pollution / ecological collapse, global heating and inter-faith relations to name a few - and more people had listened to him earlier we would as a planet be in a better place now.
As King, and with the government we have now, I can't see him keeping quiet if things head south or if they start to trample over his long-held opinions and efforts. This might cause constitutional issues, especially if he achieves political support for standing up to them (which I think would be extremely likely).