I won't pretend to fully understand it either, but self-proclaimed anarchists that I've talked to online have indicated that they do respect private and persona

I won't pretend to fully understand it either, but self-proclaimed anarchists that I've talked to online have indicated that they do respect private and personal property. A man could own a baseball bat in the property sense, but a company could not own property at all (or at least, property they expect not to be damaged by an anarchist).