Yes, mods are indeed required to uphold certain rules to ensure a healthy community. It would appear that most of the commenters here did not read the TOS for moderation. You can here https://www.reddit.com/help/healthycommunities/

Those are just guidelines. They aren’t anything that is enforced.

There is consistency and if it isn't followed then you should be able to appeal to a larger community that can ban the mod.

There’s no requirement that mods must be consistent. There is nobody to appeal to.

Sorry mods, but you don't get free reign and I don't think I'd want to be in a community that allowed such for people to be honest.

Mods do have pretty much free reign as long as they don’t break any of the very few site wide rules. If you create your own subreddit, you can run it however you want too.

If you aren't willing to do your job consistently and soberly, then don't do the job.

Being a mod on reddit is voluntary. It’s not a job.