Given you have so many hostile reps, let's take the Blood Dragons, BAF and Gaians as examples. If you were to undock and shoot 100 Corsairs, your rep with BD and BAF would be pretty good since they (and the game mechanics) consider the Corsairs as very hostile enemies, but reduce your Gaian rep as they get on with the Corsairs.
As soon as you relog or undock your ship again, your BD would remain as it was because there is no rephack but the -0.9 rephack with the BAF would make them extremely hostile to your Molly again. Even though there is a -0.55 rephack with the Gaians, this is a maximum rep so you will stay below it. Shooting Outcasts would increase your Gaian rep, but it will stay no higher than -0.55.