Remembering that I'd had this problem before (kind of) I remembered that it had something to do with TESGecko.
So I opened 'er up and merged Beautiful people, Babe Hair, and a couple of other mods I had on there too.
However, seeing no effect from this, I created patches for Beautiful people to each hair mod and applied them to Beautiful people.
Unfortunately, not only did this not work, but now my game crashes when I load my game.
For some reason, one of my mods seems to be conflicting with OOO, but it was running fine before I applied the patch so I doubt that's the case.
So now I'm sitting here, scratching my head, wondering how applying patches to a mod would make it conflict with a mod that does something totally different.
Oh, and here's my load order:
Oblivion.esm
Oscuro's_Oblivion_Overhaul.esm
Toaster Says Share v3.esm
Unofficial Oblivion Patch.esp
UOP Vampire Aging & Face Fix.esp
LoadingScreens.esp
PCSoundInnocent.esp
Adonnays Ranger Coats.esp
Living Economy.esp
ExnemEyeCandy.esp
BlackLuster.esp
CapesandCloaks.esp
KDDwemerSpectacles.esp
Scarves!.esp
ScimitarMod.esp
Wyrmfang.esp
Black Plate Armor.esp
Oscuro's_Oblivion_Overhaul.esp
OOO-No_Guild_Ownership.esp
OOO-DLT_Remover.esp
OOO-Armor_Perks_WearRate_Repair.esp
OOO-BirthSigns.esp
OOO-Combat_Skills_Perks_Marksmanship.esp
OOO-DaedraLord_Quests.esp
OOO-Dangerous_Traps.esp
OOO-Deadly_Combat.esp
OOO-DLT_Immersion.esp
OOO-Magic_Effects+Enchantments.esp
OOO-Magic_Effects+Spells.esp
OOO-Magic_Game_Settings.esp
OOO-Potions.esp
OOO-Container_Trap_Instant_Effects.esp
LoadingScreens-OOO.esp
24HrArenaAliveV2Towers.esp
gardening.esp
Alternative Start by Robert Evrae.esp
MidasSpells.esp
No psychic guards v1.2.esp
RenGuardOverhaul.esp
RealisticLeveling.esp
Seph's new animations.esp
actors_in_charge.esp
ActorsInEmotions.esp
DMC Stylish - Specialanims.esp
tkHairPack01.esp
babehair_EV.esp
Beautiful People.esp
1em_Vilja.esp
OOO-Respawn_Month.esp
OOO-Respawn_Two_Week.esp
OOO-Magic_Script_Effect_Fix.esp
Duke Patricks - BASIC Script Effect Silencer.esp
Streamline 3.1.esp
Unofficial Oblivion Patch Sup.esp
Andrews_No_Quest_Items-6729.esp
Fall hair 1+2 V.3.esp
Custom-vilja1.esp
Evantal's Dual Wielding.esp
DMCDanteClothes.esp