Confederates.
Given how slavery have been long term "issue" to the wasteland, I hope to see some equivalent of the Confederates; and I prefer them to be Enclave origin for some extra firepower.
Even if slavery was the main cause of the Civil War (and no, lets not have that discussing here), I doubt it's an issue in Fallout. It's just too common to be an issue. I would very much like to see a Southern Confederacy in Fallout, but I see them more along the lines of a ghoul and mutant hunting faction. I have actually though about that for a while and I'm still working it out. Anyway here's what I've got so far
They should use a starless Confederate Battle Flag (to not reveal the number of States under their control)
Obviously, they have a serious problem with any non-human humanoids (at least ghouls and mutants, and maybe even add robots, but NO DEATH CAMPS, THAT'S TOO MUCH)
They have units named after Civil War regiments, like elite infantry would be their Stonewall infantry, elite snipers would be the Palmetto Sharpshooters etc.
They use the Rebel Yell as their Battle cry for obvious reasons
They talk with heavy Suthun Accents, and you have the option to have the subtitles include accents as well (All o' y'all ghouls just gotta get out of our Suthun Confed'racy, 'cause we don't need no [censored] ghouls down South)
While I think Enclave origin goes too far, I can see local Enclave remnants joining them, as without a base, they'd become wastelanders themselves (not pure humans as viewed by the original Enclave). So that would force them to either go kill themselves or accept wastelanders being humans as well while still hunting ghouls and mutants, and that in turn would be in line with this Confederate attitude. I would prefer the Enclave to get their own permanent base though, as in if the Enclave makes an appearance again, they won't be wiped out again (they're too iconic to be gone IMO). Also I would like a fallout in the South to head back in time to roughly Fallout 1 and start over again.
Their very own radio station can play music like, The girl I left behind, Dixie, The Bonnie Blue Flag and much much more. Instead of playing The South Will Rise Again (Keep you confederate money even if it's made of tin) you can turn in any tin cans to be turned into a tin coins, like having $0.01, $0.05 and $0.10 being tin coins and you receive something like 10%
You can turn in Ghoul and mutant heads to receive a bounty. You can rat out ghoul encampments and lead a squad there to eradicate them. There's a ghoul sympathizing faction that dresses up as the Union and calls themselves something in reference to the CW Union. A ghoul supremacist faction might also make a nice response to Confederate politics, plus you might be able to tell the ghoul sympathizers to go rescue the supremacists, possibly resulting in the good guys being ghoulified in maybe a reactor
That's the Confederacy for now
I would however also like to see a cannibalistic faction, one that keeps human slaves as livestock to feed upon them. As a background, they come from a 2 vault experiment,involving sixual cannibalism, might be even more fun if all are addicted to hankey pankey. One vault contains male cannibals and female livestock and the other with female cannibals and male livestock. Their weapons should be named after cooking materials and they're mostly an agricultural faction, maybe even hand them part of a State. Makes you wonder about coq-au-vin doesn't it (and now I'm going to wear power armored underwear, just in case).
In general I would like to see a few evil (or Bad Karma) factions with a thorough and interesting background and along with some nice quests added to them.