For some reason, Rex and ED-E won't follow me because they each claim the other is doing the following. Also, please note that while MoreFollowers.esp may seem like the obvious choice, it's not the one causing this bug.

FalloutNV.esm
DeadMoney.esm
HonestHearts.esm
ClassicPack.esm
decwithreg.esm
Military Explansion Program.esm
rePopulated Wasteland.esm
Tales from the Burning Sands.esm
AWorldOfPain(Preview).esm
EZ_CompanionNVSE.esm
EZ_CompanionNVSE_Killable_Normal.esm
More Perks.esm
ELECTRO-CITY - CompletedWorkorders.esm
ELECTRO-CITY - Highways and Byways.esm
NVR-Strip.esm
Run the Lucky 38.esm
War Never Changes.esm
Corvega.esm
Decrucifixion.esm
Dalls_NV_Better_Faces.esp
Followers+NCR=Alliance.fix.esp
AndTheLawWon.esp
Freeside NCR Guard Post - Revamp.esp
HELIOS Outpost - Revamp.esp
IncreasedLegion1_1.esp
Mojave Outpost - Revamp.esp
NCR Embassy-Revamp.esp
NV Interiors - El Ray Motel.esp
NV Interiors - West Vegas Fringe.esp
NV Interiors - Cottonwood Cove.esp
Searchlight Outpost- Revamp.esp
Silverpeak Bunker.esp
The New Bison Steve Hotel.esp
PerkEveryLevel.esp
SecretStash80.esp
Dog_City3.esp
Goodsprings Filler.esp
Identity Crisis Part I - Silent Struggle V2.esp
NewVegasBounties.esp
NewVegasBountiesII.esp
TheCollector.esp
More Perks Update.esp
populatedcasino.esp
SaveCass.esp
Caesars_Legion_Overhaul.esp
Destruction.esp
MiscItemIconsNV.esp
Expanded Traits.esp
Vault_34_better_reactor.esp
Vurt's WFO.esp
Fellout.esp
Nevada Skies.esp
NVR-Version_10.esp
NVR-NPCs.esp
SMOTS-EC patch.esp
NVR-SMOTS-Version 10.esp
NVR_rePopulated Wasteland_Patch.esp
War Never Changes.esp
War Never Changes - Seven.esp
Poormeatandfoodprocessorfix.esp
Identity Crisis Part 2 - Long Night.esp
Living Casino Interiors.esp
Unique Items & Collectables.esp
Better Burned Man.esp
00 red cross.esp
JoeCobbIsFiend.esp
MoreFollowers.esp
Decrucifixion.esp
Decrucifixion - More Victims.esp
Corvega -Electrocity.esp
SierraMadrev11.esp
SierraMadrev1.1B.esp
AFNV_PartOne.esp
SRDG.esp

Followers + ncr mod? Have you tried some basic error testing? Disable half your mods and see if your saved game has the same problem? Rinse and repeat until the problem goes away.

If you have neither hired, I'd guess that probably somehow, the VNPCFollowers quest variable bCritterInParty is set at 1 when it shouldn't be.

open console and do (if you have nvse):
sqv 000B16D0 (that's a zero at the end)

Then hit page-up button to see if bCritterInParty it set to 1.

If it is, but neither is hired, that variable needs to be reset..