Is banning users for participating in other subreddits against the rules?

This is an alt account.

#Context

So in my primary account I mod a sub with around 70,000 subscribers. The top mod recently, (and according to the older mods she has being doing it for quite some time), has began to ban people due to them participating in other subreddits. In particular, specific political subreddits.

Our sub's modmail gets flooded with messages from the banned users about how they never even participated from our subreddit. And after verifying their post history, we can confirm this (so we have proof).

The sub has 10 mods in total with only the top mod having full permissions. Apart from her (top mod) 2 mods are inactive while the rest of us are. The 7 of us have each send multiple PMs to the top mod so we can discuss her questionable actions (We've been doing it for two and a half months).

But the top mod has not responded to any of our messages. And it's not because she's inactive. She logs in like once or twice every 3-4 days to conduct her ban sprees.

One of our mods decided to sticky a post, explaining this whole ordeal. It was up for 3 days until the top mod took it down and removed that mod from the mod list. So now we are only 9 mods.

• Is it against Reddit rules to ban people for participating in unrelated subreddits?

• If it is rule breaking, can the top mod be removed for mod abuse? If so, how exactly?