It IS possible to become neutral or friendly with the System Militia and the Red Devil Cartel at the same time, gaining access to all stations at the same time. (and the associated ships/goodies.)
(You can discount being on good terms with the Doublejacks and the Korian pirates, because you never lose access to the [mostly] law-abiding Outsider stations based on Korian pirate attitudes, and the Doublejacks don't control anythang much.)
The additional advantages of being on talking terms with all parties who count include being able to just sail right past Crime Wave investments to deliver/trade at those stations, and not having so many enroute ambushes to deal with.
The secret is that any time the attitude of either the Red Devils or the Militia moves up across the hostile/neutral boundary or the neutral/hostile boundary, the attitude of the opposing faction moves ~200 points against you.
So heres what you do:
1) In the early game, never take a mission that raises your rep with the Militia at the expense of the Red Devils, nor a mission that raises your rep with the Red Devils at the expense of the Militia. This is surprisingly hard to resist, since so many missions are structured this way, but hey, a smart independent contractor can't afford to piss off either the cops or the capo.
2) Look for missions which raise your status with each faction alone, or which raise your status with the station-owning factions at the expense of ONLY either Doublejacks or Korian Outcasts. "Deserter" & "Traitor" missions are among the best early missions to focus on pleasing the Militia; and "Red Devil Retribution" or "Interlopers!" or "Defend Captain XXXX" are among the best for raising Red Devil cred.
3) Get to Mk 1 level across the board, AND STAY THERE while working on your rep. This is because once you get everything to Mk2, the available missions seem to become EVEN MORE tilted toward situations that have you trading rep up with one faction and simultaneously down with the other. In fact, I've started keeping a full set of Mk1 gear in Surplus, in case I need to back track to some earlier style missions to repair rep later.
Caveat: It appears you can upgrade all your component systems (engines, bosters !, warp drive, sub-systems) and maybe one turret or one defense system without triggering the disappearance of the less confrontational faction booster mission types.
4) Because of the way the respective faction viewpoints start out, it is easiest to run up the System Militia attitude first. Do enough suck up missions to run it up very high. Ideally, you want it up to highest possible Neutral without going over. This is so that when you manage to push the Red Devil attitude into neutral, and the Militia outlook takes a big hit, it doesn't drop all the way down into Hostile. That is very bad (though repairable), because when that happens, you become persona non grata at all of the Citizen stations until you can get the Militia rep back to Neutral.
5) Once you've got the Militia rep up to the neutral/friendly boundary (or over, though that will lower the Red Devil viewpoint, you can do a string of missions chosen to raise the Red Devil attitude without pissing off the Militia.
BTW, the pro-Red Devil, neutral-to-Militia missions are always found at outsider stations, not at Citizen stations.
