I testet this several times by doing CSG deliver missions to Hartsfield market etc and jumping in and outside the station instance. Sometimes i could boost into the station and dock there but most of the time i get engaged by several federal security ships which made it unable to dock there for me and i had to leave the sataion again. And no i dont get shot by the station itself. But overall its to risky and exhausting for me do work for CSG in LFE stations although i get inderdicted more often by federal security ships if i travel to a LFE station.
Yes. The system authority (LFE) WILL shoot you entering their docks IF you are HOSTILE! I venture into those docks with my 6 very rarely, but am gaining confidence in my 3A sheilds. They tickle me, but never pop the shields. I agree, though, until we can get rid of these pesky LFE NPC's, it is definitely exciting to land in their stations!
If you are wanting to move missions, without hassle, run them out of Puarpris (whatever that name is...) outpost. We are still trying to flip that station.