I think a more direct comparison would be flying the US flag with a state flag covering half of it.
Personal identity flags are perfectly fine, alongside the rainbow pride flag or just on their own. Just don't cover over the "everyone" flag with specific identities. That's like the opposite of the flag's meaning.
Points for zombies:
The isolation and dread caused by the entire world turning into flesh hungry monsters, including family and friends
The body horror of being bit and inevitably losing control of your mind and having your body decay (also you can perhaps hide your infection from the rest of the group?)
There are always more, they never stop. Basically turning human persistance hunting against ourselves
Also they just make a good excuse for an apocalypse, with humanoid things to shoot