I would also add terms like "campaign" and "saving throw" to the list.
So you undoubtedly agree that you probably shouldn't be refereeing D&D, since you find that interesting, which could unduly influence your rulings and judgments? Glad we cleared that up.
Regardless. That advice is there in the 5e DMG whether you like it or not, and I suspect that things will only lean further that direction in the remastered 5e D&D.
The 5e DMG says that the DM is wearing many hats. They are not solely or exclusively serving as the referee. And when they are the referee it is in so far as they are an arbiter of the rules and having to make rulings. That doesn't mean that they are neutral when it comes to the players. After all, if that were the case, then there wouldn't be the culture of the DM "fudging" or making sure that everyone is having fun.
Nah, you can. Consider this. As a player, I am a fan of my own character. I want them to succeed. But as a player I also put my character into challenging situations because success is all the sweeter when it has been earned through hardship. But as a player I also like being a fan of other players' characters. I likewise enjoy seeing their characters overcome adversity. The same is true when I GM. Even in D&D, I am a fan of the player characters. I want to see them succeed; however, I also want to see them challenged. They may not always succeed, because we don't know the outcomes, and that's fine. Despite what you insist, I remain unconvinced that these are contradictory. When I design or run a dungeon, for example, I want the players to be challenged and I am secretly pulling for for them to succeed but I also don't (a) presume their success nor (b) put my thumb on the scale to ensure their success, because (c) as a GM I am also playing to find out what happens and I too want to be surprised.
Do you think that Matt Mercer, for example, is neutral when it comes to the successes of his players? Do you think that he isn't a fan of his players' characters?
However, I believe we generally regard the sentiment of "oh those foreign cultures and their customs are so weird!" to be xenophobic.