I mean, would you believe me if I told you that folks have done it and found it to be not only not "completely opposed to a themed setting" but actually helped
enhance the themed setting?
I'm specifically thinking here of a GM who had a player that wanted to play a Shardmind (4e psionic rock people race) in Athas. Per the GM's own words (all emphasis in original):
Case in point: I dislike the shardmind race out of 4E. I get what they are supposed to be and all, but they just really aren't to my taste. Had a player who wanted to play a shardmind bard in my Dark Sun game. I said, "Well, I don't necessarily see a place for shardminds on Athas. How do you see your character fitting in?" His reply was, "I don't know. I just want him to wake up in the desert, with no memory of where he came from. And he looks to be made of obsidian. You have carte blanche to come up with a background for him."
BAM! Not only did that give me, the DM plenty of leeway to work the character in, but gave me a hell of a hook for the campaign, too. I couldnt picture how Arshaka the Obsidian Bard would fit in the campaign at first. Now I couldn't picture it without him. That's the power of saying "yes" instead of "not in MY game."
Now, obviously, these are bespoke solutions to bespoke problems. There is not, cannot be, and
should not be, one size that fits all. It needs to be worked out between each GM and player, each and every time. Nothing less will do. But my point, as said at the start, was that things are more complicated than just "nope that contradicts the setting, not possible". Fiction is a deep, deep well. It behooves us to remember that when we claim anything is impossible within the realm of fiction.