Homebrew on this site is infuriatingly restrictive

I tried to make a zombie variant but I was told that it was too similar to the base zombie statblock for it to be published.

The reason for this restriction is to prevent people from just creating homebrew copies of all the existing content, thus making it available to everyone for free so no one has to purchase anything anymore.

Keep in mind, though, that you only have to publish it if you want other random people to be able to use it. You yourself, and anyone in your campaigns, can use it even if it's not published.

That restriction isn't very strong. For your monster to have triggered it, it must be a near copy-paste of the vanilla zombie. Try to make it a bit more different, you'll find that it's not that hard to publish it.