Protesting is one thing, because it is political speech directed at government policies, officials or actions that people object to and is quite in the spirit of the 1st amendment. The government is an acceptable target because government is the authority, it should be held accountable.
But counter-protesting is a whole different animal, ethically, because it is directed not at government which has authority, but against protestors - fellow citizens whose authority is no more than your own... that is, nil. It can serve one of two purposes- in the case where counter-protestors remain disciplined, courteous, and non violent, it is mainly a means of trying to prevent authorities from assuming the original protest represents popular sentiment. This is in the spirit of the 1st amendment.
But in the case where counterprotestors are violent, or even just nonviolently shouting over the original protest, it isn’t political free speech any more, it is nothing more than the hijacking of it in order to provoke and agitate, the same as shouting “Fire!” in a packed theater, or poking a hornet nest, as if hornets are responsible for bad policy. It’s not done in the spirit of the first amendment but rather, against it, as it is done to drown out or silence someone else’s protest, to intimidate, and so to strip others of their free speech, not to add to public debate.
The Battle of Charlottesville
This wasn't a protest or a riot. This was a set piece battle between two well equipped armies. As far as I know no private property was damaged or business's attacked. The two sides wanted at each other the police were irrelevant.