When WotC introduced Dragonborn to D&D in 4e (well, sort of - like so much else, it's complicated), they unleashed one of the fiercest but also the silliest arguments in D&D history. Because the illustrations of female Dragonborn were differentiated from the males by giving them boobs - and because they were clearly reptilian creatures, that was clearly absurd.
The reason it's an absurd argument is that these are fantastic creatures with a fantastic biology. Real-world reptiles are the way they are because they happened to evolve that way, but it's not hard to imagine that they could evolve along a different path in a different environment. And that's before we even get into the possibility of a creator deity declaring "let it be so."
Now, having said that, I do feel WotC missed an opportunity to do something different with the Dragonborn. Largely because I'm of the school of thought that non-human species should really be non-human, and that the more inhuman a species is, the more it should diverge from humanity. (And so, since elves and orcs can inter-breed with humans, that necessitates at least a physical compatibility, but there's no reason gnomes should, never mind Dragonborn, Shardminds, or Thri-kreen.)
So I would certainly have taken the Dragonborn in a different direction: rather than identify a female dragonborn by giving her boobs (and, in fairness, making her smaller than the males), I would instead have given the males a crest, much like we see in the animal world.
And, in a similar vein, I would vary the depictions for other species more significantly, also. Warforged and Shardminds would be entirely sexless, and not described as having "male or female personalities" (whatever that means). Elves, I think, would be matriarchal, with the females being larger and heavier than the males (this is already true of Drow, of course).
But there's no reason even to stop there. One could introduce a species where all PC members must be male or must be female (like the Khepri from "Perdido Street Station", where the males are all mindless drones, and so any PC would have to be female). Or, indeed, a species where sex remains undifferentiated until they enter a mating phase of their lifecycle, at which point part of the population each become temporarily male or female (and not necessarily the same each time). Or what have you.
Basically, as soon as you're talking about a non-human species, and especially once you're talking about fantasy biology, all bets are off.
Ultimately, my "non-humans should be non-human" position has a number of corollaries, some of which might be useful.
Firstly, because D&D is played by humans and therefore since even non-human D&D characters are played by human players, those D&D species should serve to highlight something about the human condition. Although there is a wide variety of human societies, by virtue of our biology we all have certain things in common - we all age and die relatively quickly; we're all driven to seek food, shelter, and sex; it's women who bear children; etc. But if we posit a non-human species with a different biology we can consider the "what if" for the case where one of these basics ceases to apply. What if elves are effectively immortal and so don't think about aging? What if plantmen have no need to seek food? What if shardminds have no interest in reproduction?
Secondly, I take the view that a choice of PC's race should be a matter of an instant - either the player comes to the process with a clear idea that "I want to play a {whatever}", or they should play a human. I particularly dislike the approach where the player chooses his class and then hunts about for the race that has the optimum ability score modifiers to suit that class.
(Crucially, though, I should note that I'm largely talking from a theoretical "white tower" point of view. In reality, players will choose their race by whatever means they wish, and I'd much rather they end up with a character they're happy with than some notion of 'pure' gaming.)
Thirdly, I'm inclined to think that the non-human species should be differentiated from humans in a handful of clear, and fairly significant, ways. An elf shouldn't just be a "human with funny ears", but neither is it a good idea to load them with a hundred tiny adjustments - better to give them four or five very clear differences.
And then, as a corrolary to that, pretty much all elven NPCs should therefore differ from human NPCs in those same ways, to build consistency in the world. An elven PC of course wouldn't be bound by those same things (since PCs are inevitably exceptional), but an elven PC probably should differ from the "human version" of the same character in a couple of ways, and those ways probably should bear some relation to the established facts - even if that relationship is to entirely subvert one of them.
(It probably goes without saying that I reject any claim that D&D is racist. It is, of course, entirely possible to play D&D in a racist manner by drawing lazy equivalences between certain species and real-world groups, but I don't accept that that is automatically the case, or even the case as-written. For the simple reason that I reject those equivalencies, and instead view the non-human species as being, well, non-human.)