"It's a peaceful protest as long as you don't engage with it". This is you. What actual reason is there for society to find this kind of attitude acceptable or compelling?

Not sure what you expect here. If you become violent in response to provocation, you are still a peaceful protester (within some limit of violence, which surrounding a car so it can't move certainly fits with).

A non-peaceful protest is one where protesters actively attack people and property that are not engaging with them in any conceivable way.

No, she literally drove the car into a mass of cyclists. She did not "engaged with it" which imply peaceful interaction.

I think it's mistaken to compare the two rather than seeing one as an extension of the other. Police already have the tools and authority to police an active riot into submission. The decision to go easy on riots is a political one motivated by a desire not to jeopardize their current powers. This doesn't mean expanding their powers is necessary or desirable even if the courts are involved however.