I think is really setting and table dependent.
"On the other hand how do you accord your friend who wants to play a drow or bugbear and walk into town."
I can't answer in the general case but...
Drow are in my setting extinct. Ok, they aren't, but that's a campaign level secret that would be specific to a particular game where and how it was revealed to the players that some Drow survived the Kinslaying. The Drow and the Kinslaying are such remote events from a human perspective, that most humans have never heard of it and if a Drow walked into a human village or city, they wouldn't be recognized as a Drow but would simply be presumed to be an elf or half-elf. The average elf, first seeing a Drow in a human village would think it was some sort of sick prank, and be offended, and only get murderous once they realized it wasn't. Generally speaking, I would not accommodate a friend who wants to play a Drow until after that friend had played in a campaign where the existence of the Drow was revealed.
Bugbear in my setting are goblinkind, and as such are one of the Free Peoples. There are parts of the world where a Bugbear would not at all be out of place on a city street or sitting at a bar. I wouldn't accommodate a friend who wants to play a Bugbear because they are a +ECL race, and I don't allow +ECL races as PCs normally because balance is complicated. But, there have for example already been a couple hobgoblins in the party. I generally allow players to play hobgoblins or goblins if the starting setting accommodates that easily. If I was planning to start in a setting where the level of goblin xenophobia was high, then I probably would take them off the table. Of course, there are areas where the level of elf xenophobia is pretty high as well, and I might consider taking them off the table for some campaigns.
In general, your question is a subset of the general issue, "What if the player wants to play a bug-eyed monster with a "heart of gold", or at least a lot less of the general monstrosity associated with bug-eyed monsters."
And for me the answer to this is, carefully. Make it really clear up front that the player will provoke a lot of hostile social responses and be generally treated as a second class citizen at best, and as a sort of monster to exterminate at worst. Have a solid set of mechanics in mind for how you plan to fairly arbitrate how that will actually work so that you aren't just always relying on fiat, but will have a fair mixture of responses from NPCs. I generally give flat xenophobia penalities on all social rolls, to PC's of a race interacting with another race. And I generally will start anyone that looks "wierd" one or more levels of friendliness below normal. Expect a lot of, "We don't serve their kind here!" and so forth. For sorcerers, which are in my game rather close cousins to the X-Men in a supers setting, this is often built straight into the class depending on the chargen choices you make.
The main problem you run into with a character playing a bug-eyed monster with a heart of gold, is that it's very easy for that one player to dominate all of the party's social dynamics, motivating the party to either always leave the character out of play, or else making the character always the center of attention. So either you have to run a Star Wars cantina setting were no one really cares, or you have to have a pretty mature player.
