I was a mod before, but I suppose it was a few years ago now. I was sent a list of rules (types of posts that should be deleted), but to be honest, I found being a mod rather difficult because there is a lot that is left up to subjective opinion.
Some posts are easy to delete, like ones that are obviously spam or harassment.
With others, I struggled a lot more with deciding whether or not to leave them because my ideal GAG was one where people could be free to ask and discuss things, to debate, and maybe even change people's minds.
I'm a feminist and an atheist, for example, and knowing that that was my bias made it even more difficult to decide what to delete and what to leave. At the time (I've been away for awhile, so I'm not sure what things are like now), there was A LOT of woman-bashing going on (it was actually one of the reasons why I eventually decided to leave). So, while part of me wanted to delete all those questions/comments because I felt they made this site rather toxic for women, I also didn't want to go all authoritarian and delete everything I didn't agree. I tended to err on the side of leaving things up, and if another mod decided to delete it, well, it is what it is.
I tried to be fair, regardless of the topic and my personal biases. Attacking an individual user? Not okay. Saying something shitty about a group of people? I'd generally allow it and hope it would generate some good discussion, as long as it wasn't too inflammatory (for example, if someone went on a rant about black people and was calling them the n-word, I would delete it).
Anyway, what it comes down to is this: mods are just regular people, all with their own biases, following a set of rules that isn't cut-and-dry, and so their biases are going to come out, especially if they aren't conscious of their biases and actively trying to be fair.