Same with the player wanting a specific input. It is not limited to race "I want to play a sea elf" is simply a player preference that can be as disruptive, or as harmless, depending on the campaign, as any other background proposal. "I want to be the crown prince" isn't different from "I want to be a bullywug" or "I want to experience being the victim of racism and nazism in 1930's Germany in your Indy-punches-Nazis campaign". The GM has something in mind, can, in good faith, try to accomodate player input, but there is some point where it will change the core of the game too much to his liking, so he'll say no. No doesn't mean "I hate you" or "bow before me", just "I don't want to go that far in this particular campaign, because it wouldn't be fun for me to do that". If it is established that the depth dwellers are all sahuagin, then the first sea elf to appear in the setting will, if not killed on sight, be a strange and unique creature that will gather the interest of every academic institution in the world, much like a sea elf arriving in our world, and it is becoming a main theme of the campaign much like the crown prince player would. If it's a world with 60 races and no special care about their relationships between each other, then sure, it's not very disruptive to have an until-now ignored sea elf appearing...
I can't see any amount of consensus force a player to play a character he doesn't want, and force the GM to run a campaign he doesn't want. Both have the right to have the fun they want. So as a player, if you want to play a bullywug to have fun (and can't have fun with the constrained list that is offered), you need to find a campaign where having a bullywug PC is possible, and as a GM, if you want to run bullywug-free campaign to have fun, you need to find players willing to play it.