We do not live in a democratic republic. People seem to be confused on this point.
We don't live in a democratic anything.
Having a king with actual powers means it's not a democracy.
Some are either happy to keep things as they are, or perhaps don't appreciate that we are being fooled by the establishment.
Others want things to change, to modernise and progress. We, as a grown-up nation, should debate and consider this. The establishment doesn't even want the debate, presumably they know that their position is untenable so the only way to win the argument is to suppress other ideas.
Most people don't particularly care one way or the other about royalty. There are fanatic royalists, those who want a republic and probably the majority who don't care strongly either way. But I suspect that many could be persuaded to the republic side of the argument if we discussed it openly.
All MPs are required to pledge allegiance to the king, and debate about the king's position in the country is not allowed in parliament, at all, ever. So there is no democratic route for those who think we should change, therefore protest is the only way to present an alternative opinion. If the right to protest is taken away then there are no other legal options.