Lots of great thoughts in this thread. Not sure I have much to add to what a GM's responsibilities are, but I have some thoughts on what they are *not*.
It is not the GM's responsibility to:
1. Babysit. If you want your kids to play in public games, you remain responsible for them. I say this as a parent. I'm not anti-kid. But I have too much to pay attention to that it would be irresponsible for me to even give the impression that I'm going to look out for your kids.
2. Provide therapy. I believe that as GM, like in other contexts of life, I should practice good etiquette, strive for politeness, and in public games with strangers avoid politics and commonly objectionable content. But my games are not for you to work through whatever issues you might have. TTRPGs *have* been used in therapy, but the primary role of the *those* GMs is a therapist. It isn't the expected role of the GM running the typical game.
3. Run the game exactly as you see fit. Even in organized play, there are different play styles. If you don't like my style, that's okay. Find another table to play at next time. But don't give the GM grief or get in the way of other players' fun because you wanted a hack-and-slash and not urban intrigue, or you a want role-play heavy game, not tactical battles.
4. Know all the rules perfectly, at the tip of my finger. Unless they are completely new to the game, players have a responsibility to know the basic rules and the rules pertaining to their characters. I have enough to keep track of as the DM. I've had players who have never played before coming to the table with dice, sharpened pencils, and a copy of the PHB. So, I have little patience for players who come week after week and have to keep borrowing dice, don't bother to even print the free basic rules, and waste everyone's time because they don't know how their characters' abilities work and blame the slow down on the GM.
5. Put up with bad behavior. I see it as my responsibility to be open, welcoming to diverse types of players, and to try to make sure we are all having a good time together. That doesn't mean that I have to put up with players with terrible manners, poor hygiene, or who are abusive to other players. This is contextual. In many game stores, there are strict rules about language. I'll enforce them because I want the game store to continue to allow me to play there. My home games are R rated. But they are not X-rated--my home, my rules.
Have I missed anything? Are there other unreasonable expectations some players have of non-paid GMs?