It's kinda seemed to fall on a continuum.
1) At one extreme, the DM decides, and the players need to live with that--their preferences in this instance don't matter.
2) At the other extreme, the players bring their characters, whatever they are, and the DM lives with that--their preferences in this instance don't matter.
It's seemed to me as though there's remarkably little actual clustering at the actual extremes: I think
@Maxperson and
@Oofta have expressed a willingness to work with players in finding stuff that fits in the world/s they run, and
@Zardnaar runs some games with tight themes and some that are anything-goes; and even some of the most ardent player-rights posters have expressed a willingness to accept (or impose, when DMing) some limitations on what is available in a given setting or campaign.
I think that what's happening mostly is that a poster says something like "I don't allow Warforged on my world because I don't want mecha in my D&D game" (it me) and people from closer to the player-rights end of the spectrum focus fire; Fact is, while that's probably the one race I'd stand hard on rejecting (along with anything that flies at 1st level), I'd talk to the player about why they want to play a warforged and poke around and see if there's something I will allow that gets at those reasons.
@Chaosmancer and I had a little talk about Changelings, and I think we found some common ground that if the draw of playing a Changeling is "I look human but I'm not" then I have something already in my world that does that.
I will say that wen I set up my world, I made a specific decision to allow everything in the PHB (well, other than Drow) because those were in the core book, and it seemed reasonable that someone new to the game--I was setting up a table at my FLGS--would have that, and nothing else. I have been a bit more choosy about other things I've allowed, based on how the world has taken shape and what's made sense to me--which is almost certainly derived from my own preferences. There are races that I look at and kinda say "nope." As I have said, though, the world I'm running has porous planar boundaries, even by typical D&D standards, so something from outside can arrive; if a player is willing to work with being the only adventurer of their kind, the races I haven't written into the world are technically available for play. If they're looking to play based on some stereotype--either leaning into it or rebelling against it--that's not likely to work for, e.g., a kenku, but there are other approaches available.