This is an issue that has always existed in ESO but really needs to be fixed. If you are on a quest that makes use of disguises having a pet out makes the disguise not work properly.
If you get near a Sentry NPC that can see through your disguise the eye opens partially giving your warning to move away. However, when this eye opens like that, you are instantly in combat mode. This means any combat pets you have out will go attack that sentry, thus breaking the disguise.
The combat mode also affects non-pet users since it prevents using objects, doors etc.
It would be best if Sentry NPCs did not put you into combat mode unless they actually attack you. Since you haven't actually been detected when the eye is only partly open, there should be no combat.