So a number of years ago I joined a campaign with a DM who decided to lean into the fantasy racism angle. It was a setting where there was a collision of the planes and a bunch of different races were thrown together for the first time and a bunch of nations were very reactionary and became deeply suspicious of other races. I decided to play a dwarven unity (the UA form of what later became peace) cleric who was actually saved by a genasi and his whole personal goal was to foster a culture of acceptance and understanding and bring the various races together in harmony.

So in that setting and that campaign it was highly appropriate to highlight the reaction of the various NPCs to exotic races and to have lots of roleplay about racism and such. And even with that I ended up retiring the character halfway through the game and we as a group decided to downplay the fantasy racism angle because even with a character that had a personal goal focused on combating it, the whole thing was repetitive and boring at best and brought up uncomfortable real world issues that upset the people sitting at the table at worst.

Since then when I DM a game I generally take the fantasy kitchen sink approach. If you want to play a warforged or a goblin or a centaur go right ahead. The narratives, settings, and campaigns that I like to run are agnostic about race and in my settings no player is going to be negatively singled out because of their race. Players are free to lean into it or ignore it as much as they want and if I get the sense that they want to do more RP based on their race I'll indulge them, otherwise it'll just get passing mentions and otherwise not be an issue. When I join a campaign as a player I'll be sure to bring up the issue of fantasy racism and what kind of reactions I might expect if I play an exotic race, if they tell me that I can expect a negative reaction I'll ask if we could downplay that (for the aforementioned reasons).

I think there are two reasons players pick exotic races:
1) they want some special ability from that race, if you're OK with that special ability you could just transfer it to another race for that PC. Treat it like a unique thing for that one character.
2) they want to make an interesting character, and using exotic races is a cheat code for that. I think those players are in for a bit of disappointment, it's the roleplaying that is (or isn't) interesting, a funny hat is not.

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On the question of "Or do we just ignore the PHB and kitchen sink everything?" No. Talk to players. IMO player characters should be made in collaboration with the DM. Otherwise you are guaranteeing that the character won't really fit the setting, the campaign or even the party.
Mastikator, I think you're generally correct in saying that people pick races either for the abilities or as a shortcut to making an interesting character. And certainly you're correct that it's the roleplaying that makes a character interesting and that the DM and players should discuss the characters beforehand to make sure it fits because not everything will fit at every table. However I think you are overlooking the fact that having an exotic race enables certain roleplaying elements that might otherwise be impossible. It isn't inherently more interesting to play as a centaur or a warforged or a plasmoid or whatever but those players have options to explore in their roleplaying that the elves and humans don't and that can be a lot of fun for everyone.

So of course talk to the DM and pick something that fits, if you want to be a human in the building a monster town campaign that's probably not gonna fly. But also if you're a DM try to be a little open minded and work with your players to make something fun and don't automatically shoot down everything. And definitely don't punish players for their race unless you've cleared it first. We get enough of that junk in real life, no need to foul up game night with it.