I can even talk to hostile NPCs, because they can take 5-10 seconds to recognize me as an enemy and start attacking. I guess it's because some mod I have, or a conflict. I have this problem since some time ago, but I never cared much because I was playing a thief and rarely went to dungeons. Here are the mods:

GameFile0=Aduls_Master_Mod.esm
GameFile1=Bloodmoon.esm
GameFile2=MCA.esm
GameFile3=Morrowind Patch 1.6.5 Beta (BTB Edit).esm
GameFile4=Morrowind.esm
GameFile5=Tribunal.esm
GameFile6=TR_Data.esm
GameFile7=TR_Map1.esm
GameFile8=TR_Map2.esm
GameFile9=adamantiumarmor.esp
GameFile10=Adj_Magicka Regen (0.50%).esp
GameFile11=Aduls_Arsenal.esp
GameFile12=AK_PCClothier_Balmora.esp
GameFile13=Always +5 Modifier.ESP
GameFile14=Antares' Big Mod 5.3.esp
GameFile15=AragonMonk-v10.esp
GameFile16=B79_RacersRoost_v1.1.esp
GameFile17=BalmoraStockExchange_0925.esp
GameFile18=bcsounds.esp
GameFile19=Bloated Caves.esp
GameFile20=Brittlewind_Fix.esp
GameFile21=BTB - Alchemy.esp
GameFile22=BTB - Character.esp
GameFile23=BTB - Equipment.esp
GameFile24=BTB - Settings.esp
GameFile25=BTB - Spells.esp
GameFile26=CalderaFightClub.esp
GameFile27=Complete Morrowind - Tribunal & Bloodmoon.esp
GameFile28=Complete Morrowind TB & BM - Replacer.esp
GameFile29=CS Studios Petshop.esp
GameFile30=Dread.esp
GameFile31=EBQ_Artifact.esp
GameFile32=EcoAdjDaedricDrops.esp
GameFile33=entertainers.esp
GameFile34=Graphic Herbalism.esp
GameFile35=Illuminated Order v1.0 - Bloodmoon Compatibility Extras.esp
GameFile36=Illuminated Order v1.0.esp
GameFile37=Improved Gold Weight.esp
GameFile38=INDYBANK.ESP
GameFile39=LeFemmArmor.esp
GameFile40=master_index.esp
GameFile41=MCA - Guards Patch.ESP
GameFile42=MCA - TR Addon.ESP
GameFile43=MWE_Base.esp
GameFile44=MWE_Writing.esp
GameFile45=Piratelords Trade Enhancements.esp
GameFile46=Quarra Quest Fix.esp
GameFile47=Realistic Weather v2.0.esp
GameFile48=Siege at Firemoth.esp
GameFile49=Skooma Anonymous.esp
GameFile50=SQD_Vile_VampHider.esp
GameFile51=Sris_Alchemy_BM.esp
GameFile52=Suran_Underworld_2.5.esp
GameFile53=The Broken Drum 1.01.esp
GameFile54=TravelingMerchants-1.2_BETA.esp
GameFile55=Vampire Alchemist.esp
GameFile56=Vampire Hider.esp
GameFile57=Vampire Realism II - BM Add-On.esp
GameFile58=Vampire Realism II - TB Add-On.esp
GameFile59=Vampire Realism II.esp
GameFile60=Vvardenfell Druglord.esp
GameFile61=Wayfarer's Rest v1.21.esp
GameFile62=Westly's Master Headpack X.esp
GameFile63=ZAS1.esp