I think the Ancaps are waaaaay to patient with the budding progressive movement, considering they left terra to escape all that nonsense. Not that they have to initiate any form of violence, but just walk out of the room after the first couple of outrageous demands.
I mean, it's not like any of the progs have any higher power to appeal to to initiate force upon the businesses to heed the groups demands, right?
Ignoring the progs might event bring them to attempt violence in the form of terrorism, which would then give the adcaps the right to protected themselves and all but eliminate the progs, if not at least exiled them.