Turning into a zombie changes the perception of the creature. They often act as if they aren't aware of each other. Even when they are swarming, you see zombies climbing over each other, trying to reach the living. They are not working together, so much as they are all after the same objective.
The change in perception could make them see other zombies as allies (or harmless / non food things) as opposed to the living, which are food. In I Am Legend (the novel, which influenced and popularized the concept of zombie apocalypse) the infected saw un-infected as monsters / food, and saw each other as normal.
From Wikipedia I Am Legend Novel
..but fear and hate Neville, who has destroyed some of their people along with the [dead bodies animated by the germ], during his daytime excursions against the latter.
You might say being infected makes normal humans look like this:
Taken from Cracked
Personally, I was making a lot of progress in my weight loss over the past week, ever since that big biohazard emergency. I guess the mandatory quarantine has helped keep out distractions so I could really focus. The weight has literally been falling off of me, like in actual chunks of flesh, which is a little weird, but I guess that makes sense, how else would fat people get thinner?
The only problem is that lately I just keep running into really delicious looking people, just really pink and fleshy, with brains that just melt in your mouth. They have to be like, a million calories. I guess I just need to start avoiding bunkers and fortified buildings entirely, since they're always chock full of tempting, tasty-looking people.