I spent quite a bit of time at the nav beacon in my local anarchy system and I am still neutral with the system's factions. No one shows a bounty, but I kill warrant scan them and then kill the ones that have a bounty from somewhere else. I only shot one or two ships without a bounty that I accidentally got into a fights with.
On the other hand, the resource extraction point in the system has authority ships. I avoid it because for some reason they want to shoot me when I start fights there. I imagine shooting those ships might have some faction implications. I think the devs haven't fixed extraction points to work properly in anarchy systems, otherwise why are there authority ships?