I've recently discovered that it isn't about the racial and class options; it's about the players.
I absolutely agree with the posters in this thread who have said that the most important thing is that the dungeon master be comfortable with the verisimilitude of his setting, and that he therefore has final say on all player options in it, but what I've found is that even if I've decided up front that there will be no drow gunslingers in my campaign, the right player approach can change my mind.
Right approach: "I have this great idea for a drow gunslinger, here are three pages detailing his history and can I buy you a chai while we talk for an hour about how to fit him into your world?"
Wrong approach: "I have this great idea for a drow gunslinger, Drizzt is awesome and guns are awesome."
Worst possible approach: "I have this great idea for a drow gunslinger; this feat and that archetype and multiclassing here and here, and 40 gazillion damage without having to roll to hit."
I may not /want/ drow gunslingers in my party, or even in my world, but the player with the right approach is going to make the campaign better, damn him, and denying him doesn't actually /accomplish/ anything. I have decidedly mixed feelings about how rare this sort of player is.
I just did a light conversion of Dragonlance to D&D5 and I made room for tiefling, dragonborn (draconian) and warlock characters because I trust that my players are of this type. Does it make me nervous? Sure, but I've come to trust my players and take that nervousness in stride.
I guess what I'm dancing around is that there is no fairness in dungeon mastery. I've always felt this way about play, and I don't know why it took me this long to apply it to character generation. But just because I let player A play a drow gunslinger does not mean that I am obligated to let player B do so. Just as I can rule on success differently for the two players based on circumstances in play, there are extenuating circumstances in the metacampaign as well.
It's important that my campaign world have internal logic, but it is also important that I be open to external ideas, so long as those ideas come from people who have proven themselves. The end result from such moderated interaction can only be improvement.