Zombies that fixate on villagers in the area totally ignore player regardless of how close the player is to the fixated zombie. I have walked up to several zombies, which were fixated on villagers in a house, and I pushed them around but took no damage. This also occurred with a zombie that was much closer to me than to any villager (about 40 blocks away and 3 blocks higher than the villager). The zombie came up to me, did no damage, started walking away from me toward the villager. So I hit it with my sword. The zombie then became fixated on me and began doing damage. I killed it.