It's the DM's right to allow or disallow races, classes and so forth from their game. If a player doesn't like it, I'd say it might be time for them to DM their own campaign.
We just started a new campaign, and for the first time I'm allowing all the PHB races. I've never before allowed elves or gnomes. Fortunately, no one is actually playing an elf. For some unfathomable reason though, one of them is playing a half-elf. And another is playing a gnome who doesn't like to bathe. Since the player does bathe though, I think we can all handle it.