I think "protester" is appropriate for people who are protesting a political process in a political building - even if some of them exceeded acceptable behavior, committed crimes, were violent etc.

Using BLM as an example, is it still fair to call them protesters though they sometimes fight with police (violent behavior), graffiti or break windows (vandalism), loot (breaking and entering)?

Sure, I agree. But this thread is specifically talking about the subset of the protestors who were committing crimes. No need to call that subset "protestors".

BLM vandals stormed Oregon State Capitol. They also established autonomous zone where they had their private security shooting two black teenagers.

Are you sure about this? The link you yourself shared shows photos of people carrying "thin blue line" flags. The quotations inside the article you shared says "Just before their violent physical assaults on journalists, the right wing extremists literally tried to kick in the door of the Oregon State Capitol in Salem".

Here is the link you shared in a sibling comment: https://deadline.com/2020/12/armed-protesters-enter-oregon-s...

Thanks for noticing, you are right, i mixed the two events. The BLM rioters breached a court house in Portland [1], while the other side attacked the state capitol in Oregon.

[1] https://nypost.com/2020/07/26/portland-protest-declared-a-ri...