When you get into a Conflict Zone, yes if your REP with them are hostile, they show up red, BUT after you choose sides on the comms panel, they turn friendly, and after each CZ is totally finished, you gain REP by the zone size, I believe its REP+ for low, and REP+++ for high CZ.
So if they're hostile, don't go in their station just yet, go into CZ, you should turn into unfriendly with 2 high CZs, or maybe.. 3 or 4 low CZs.
Which they will not attack you and allow you to dock when you're unfriendly with them, the station tower will just say something like "Make your visit short CMDR."