The difficulty I have with this statement is that a player who is unhappy with elements within a campaign has the opportunity to avoid them or, if all else fails, to leave the game. I may not like tieflings. I may really hate there fluff and implementation within the game but if another player insists on playing one I might find it irritating but it isn't that much of a problem. I can even turn it into an advantage by creating dynamic tension between our characters. This will be disruptive but probably not fatal to the game.
The DM doesn't have these lesser options. If the DM is unhappy with elements of the campaign world and the players insist on using them, which you say they should be able to use. He can't avoid those elements. If he hates tieflings and a player insists on playing one he can't ignore them and has to deal with their imprecations on the game. If a DM leaves the game than, usually, that campaign is over.
My rule in general is that the DM being happy with a campaign is more important than any particular player being happy with it because an unengaged player is unfortunate and will damage the game but an unengaged DM will kill it.
One presumes a good DM who is only happy by taking into account the desires of their party members, and sets clear reasonable limits that they live within. You set very clear lines. Your rule as quoted makes a lot of sense. Most of what is being discussed here seems to be the unusual cases. Your tiefling example wouldn't be a problem just for the DM, but for the rest of the party who agreed to live within your limitations.
The OP has since learned that there was a decision about naming that they somehow hadn't known of. So they are agreeing to abide by the DM's limits, it sounds like. There is no way to know whether the situation is reasonable or not.
Based on "He then said that he thought the difference between his idea of light-hearted and mine was because I am a woman. *rolling my eyes*
Lastly, he said he would not compromise, and, the part that really stuck in my throat, was when he said, "if I'm going to spend hours upon hours preparing a game so I can DM it for other people, my enjoyment needs to come before theirs." This, I don't get. I'm not just some pawn in his world, there to play for his pleasure. We are all in this together. Doesn't it need to be fun for everyone?"
So perhaps this DM as presented isn't so good.
1. Not particularly open
2. Lacking in some flexibility
3. Not clear about the limitations (since Architectofsleep didn't know of the naming limitation), which seems obscure since you need to choose names the DM finds acceptable.
4. I personally find it offensive that the DM (based on #3), insults the OP by basing the difference in taste on gender. Perhaps this DM has not caught on to the idea that since AD&D there aren't many in game rules that are gender based (drow excepted), and all the rather significant implications of those changes. Since I usually game with guys I find there are gender differences in how we play- seems quite reasonable (although I never heard of being a female gamer as an asset?) So this DM would drop in my estimation (especially considering he is DM to a mixed party.)
And most importantly to me, it isn't clear what makes the game enjoyable for this DM, lots of control perhaps, but that is too general a statement - micromanagement perhaps is better. The problem with the statement is that the DM needs to enjoy the game, and the only person who can really affect that is the DM. The players can only do so by staying within the limits of the game.
To me what is most enjoyable is in succeeeding in making the game fun for the players. Different goals for different DMs I guess. It sounds all very subjective, which makes your quoted rule very difficult.
So then the question becomes what makes the DM happy? (Generally by polling your players and watching their style of play, a DM can figure out what makes them happy.)
(your (ex) tiefling)