It’s one thing not to like illegal protests and a different one to equate them with anarchy. I understand that the term “anarchy” is often used as a synonym to “lawlessness” but in reality it is a movement that aims to eradicate societal hierarchies and replace them with horizontal organizational structures.
Also as I’m sure you know, law is not set in stone, it does change. Many things that are legal now, were illegal in the past. Sometimes in order to influence lawmakers we need to do illegal stuff, like non-violent disruptive protests.
If you want to change the law, you contact politicians, sign petitions, protest in a way that doesn’t prevent emergency vehicles or public transport from reaching their destinations, and you vote during election. If that isn’t enough, you run for office. Doing illegal stuff isn’t justified at all.
That’s appropriate when you’re trying to change certain things, not everything. When you’re trying to get civil rights or anything else that the higher ruling class doesn’t want you to have, it can and usually does necessitate illegal and violent protesting and uprising.
Of course what you describe is a way of doing things. What you say and what I said are not exclusionary. People can have both legal and illegal approaches on the same topic. Sometimes it is justifiable on moral grounds to break the law, and many countries recognize that need in their constitutions.