Mobs can't pathfind through open doors.

Works as expected

• if the doors are wooden and the mob is a villager or zombie (villager) with CanBreakDoors:1
• if the mob is a zombie (villager) and it has a villager as a target
• if the mob is a baby zombie (villager)

If the only way from mob to the target goes through open doors, the mob stays behind the doors and follows the player's movements (see the Animation.gif)
If there are 2 ways from a zombie to player, one through open doors and the other without them, the zombie chooses the second way.
Steps to reproduce:

1. Build a room with a door (a place, which can be exited only through door(s))
2. Summon any mob in it, that can be provoked / led by food.
3. Make sure the mob (normally) can come out of the room.
4. Open the door.
5. Provoke/take needed food in your hand/go far enough away.
   The result: the mob will be stuck behind the door.