Tested on a single-player world using a bow. I got very close and personal to an Iron Golem and tried firing an arrow. Sometimes the arrow went right through the Golem without dealing damage to it, but it did damage to the next entity behind it.

My guess would be that there is code in place that prevents the arrow from hurting the player when it spawns, since it seems to spawn partly from inside the player. I think if the collider of the arrow overlaps with the entity's collider when spawned, that also applies this behavior to that entity.