See, my problem is when you phrase it like that. "Allowed"? It's not a case of being allowed to do anything. It's a case of coming together to find a common ground.
I mean, would either a Hobbit or a Vulcan actually be a problem in a Star Wars game where rabbit people are canon? Now, if you want to play a Vulcan, complete with Star Fleet and a Federation ship, then, sure, obviously that's not going to work. And, speaking purely for myself, I find I'm a lot more flexible when I realize that my choice is going to dump a bunch of work on the DM's lap.
For example, if you're doing a real Man Vs Nature style campaign where tracking food, water, disease, that sort of thing is a major element of the campaign, I'm a lot more willing to give up my Warforged character since that negates a major part of the campaign - doesn't eat and is immune to disease? Well, maybe not a good fit for this campaign.
But, OTOH, if we're playing Star Wars, and I want to play a pointy eared humanoid with a logic fetish, the DM can probably live with it. If the DM really can't, then, well, as I said earlier, it's not a deal breaker, but, it does send up some red flags.