One of these mods causes the problem. I think it might be one of the mods that affect all NPC's, like the faces or clothing mods. I am still looking around for possible patches.
My modlist:
_001_ Morrowind.esm
_002_ Tribunal.esm
_003_ Bloodmoon.esm
_004_ Morrowind Patch v1.6.4.esm
_005_ THE Facepack Compilation.esm
_006_ Better Heads.esm
_007_ Better Heads Tribunal addon.esm
_008_ Better Heads Bloodmoon addon.esm
_009_ Texture Fix - Bloodmoon 1.1.esm
_010_ VGreetings-Hit.esp
_011_ IceNioLivRobeReplacerALL.esp
_012_ Better Clothes_v1.1.esp
_013_ More Better Clothes.ESP
_014_ VGreetings-Thief.esp
_015_ VGreetings-Flee.esp
_016_ VGreetings-Idle.esp
_017_ VGreetings-Attack.esp
_018_ VGreetings.esp
_019_ Traditional Vampire.esp
_020_ Animal Behaviour.esp
_021_ WeatheredSigns.esp
_022_ Dodge Mod 1.2-WD (Enhanced-LD) (Tribunal).esp
_023_ Armor Effects-LD 2.0-WD.esp
_024_ Vivec_Voice_addon TRIBUNAL.esp
_025_ Dagoth Gares_Voice_addon v1.1.esp
_026_ Clean Better Daedric.esp
_027_ Dagoth Ur Voice Addon.esp
_028_ DB_Attack_Mod3.esp
_029_ Almalexia_Voicev1.esp
_030_ barilzar_voice.esp
_031_ Better Bodies.esp
_032_ werewolfrealism-moononly.esp
_033_ Cloth Bracer Alter.esp
_034_ Clear Ice.esp
_035_ STA_guides_replacer.esp
_036_ EcoAdjCrime.esp
_037_ LeftGloves.esp
_038_ Clear Glass.esp
_039_ drenbalance.esp
_040_ EcoAdjDaedricDrops.esp
_041_ Vampire_dreams_reduction.esp
_042_ Steel Broadsword Fix.esp
_043_ Psy_UniqueDremora_T.esp
_044_ TownSounds.esp
_045_ Improved_No_Glow_v1-MW_Trib_Blood.esp
_046_ NighttimeDoorLocks-LD 1.1a.esp
_047_ elfheight.ESP
_048_ k_weather (louder sounds).esp
_049_ k_in_tent.esp
_050_ Fair Magicka Regen (one Percent).esp
_051_ DodgeTribunal-v21.esp
_052_ Sound Enhancements.esp
_053_ Charming Ash Vampires.ESP
_054_ BAR_CreeperMudcrabRemover.esp
_055_ Moreclasses_0605.esp
Elfheight is a little mod of my own design that makes High Elves a bit shorter.
I tried to fix it with the editor by replacing the Beserkers' class (Acrobat) major skill Unarmored with Medium armor. I thought that perhaps the Unarmored skill prevented them from equipping any armor, so I created a mod that changed this and put it upfront in the load order. It made no difference however, so that approach at leastdidn't fix it.