What I expected to happen was...:
Iron golems would instantly attack any zombie within its radius

What actually happened was...:
The golem did would sometimes do absolutely nothing and continue to wander about. Sometimes it would completely ignore the zombie while being attacked by one.

At first I thought it was I was playing with mods. To test for this, I copied my modded survival world and opened it in Vanilla to test to see if the same issues existed. Turns out it happened also in Vanilla. This only happens with some of the iron golems. I don't know if this should be considered a bug or not, but I believe it is one.

Steps to Reproduce:
1. Spawn some zombies around an iron golem or 2
2. Wait to see if the golems will attack.
OR
1. Wait for a Zombie siege to occur
2. Then wait to see if the iron golems will do anything about the siege.