General off topic question: what happens if someone new joins who wants to play a dwarf? Because they weren't part of the group on the onset and no one chose a dwarf, now the player is out in the cold?
This rarely happens. But yes. Once the campaign is established, it has features. I make exceptions if I can, but if I can't, then I don't. This tends to mean that "one-off" characters work better than established races: a warforged who's the only one of his kind is easier to justify than a random gnome.
This rarely causes problems because 1. I rarely have people join mid campaign, and 2. when you tell the possible new player, "well, the PCs are elves and dragonborn, their countries used to be at war about a generation ago, but now they're trying to get along, and the players are investigating an island that used to be a colony from the elvish nation, but everyone on it disappeared during the confusion of the war, and the dragonborn were blamed, but now it looks like they weren't even involved, and whatever killed all the colonists might be back... so, yeah, can you make something that fits into that?" They generally say, "sure, sounds good."
If you give someone an actual reason why they can't play something, they almost never object. If the reason is "I hate X so you can't play it," you might have a problem. If the reason is, "There are no X in my campaign world I just made up two minutes ago, and no, I can't put any in," then they'll figure out that you really mean "I hate X so you can't play it," and you might have a problem. But if you give them an actual reason that doesn't boil down to you using your power as the DM to impose a pet peeve on someone, they almost never even consider complaining.