Well, yeah, a bit like how you can put "Half-Elf" in the race field but play it like a Human or Elf aside from minor mechanical differences.
I think that this actually gets to the heart of it, both on the main topic of the thread and the side discussions that we've been having. Yes, we can. And that's not only 'Ok', but inevitable.
There is no one in the world that can play an authentic Half-Elf. There is no one in the world that can play an authentic Elf. This is obvious and I would hope uncontroversial. These things are self-evidently true because elves and half-elves aren't real, so no one can speak to the authenticity of being an elf. I can give my players a 10 page document describing in a very high level overview elven culture as it pertains to my wholly invented imaginary world, in hopes of sparking some amount of creativity in them, but I certainly can't claim my take on elves is authentic. There is no standard to judge authenticity by.
Nonetheless, as the DM, I have a responsibility within the game to be every other single being in my creation who isn't a PC. I have to be all the men and all the women. I have to be all the fair skinned people, and all the dark skinned people and all the peoples whose ethnicities and even species have no parallels in the real world. I have to be all the saints of my world and all the most dastardly villains. I have to be all the gods of my world, and all the lowest peasants. I have to be the abusers and the oppressors and the abused and the oppressed. I have to be the pretty people, and the low charisma people lightly regarded within the world. I have to be the proud and the humble, high and low, the meek and terrifying dragon fuming arrogantly in his lair. I am every single extra in the story, and I am the villain that chews up the scenery that everyone loves to hate. I'm the mentors and the henchmen and literally every character in the story but the protagonists. The PC's get to decide who those are.
I don't feel like I have any particular obligation to anyone but my players regarding the world I create and the stories I tell, but it is my pleasure as the creator to fill the world up with as diverse a cast as I can manage. I shall be very put out if someone comes and tells me that I can't do so because I'm not authentic enough to pretend for a little while to be a woman, or a child, or an old man, or a Tumesi, or Elven, or Mokoheen, or Averen, or a Har peasant patriot with a foul mouth, a swaggering Orine bravo, or a Sea Folk Wise Woman puffing on pipe, or a goblin prospector seeking out wealth, or a barbarous merfolk girl hunting gulls, or a 4000 year old incarnation of the spirit of a bitter well, or any other darn thing that I think of that I think makes my world a richer place for their presence. And I shall be even more put out, if I'm told that I'm not authentic enough to do these things, but that I didn't do these things that the absence of "diversity" in my world reflected somehow on what I thought of people in the real world. There would be no way to pass this test, and I'm arrogant enough to think that the real world would be slightly less rich and interesting of a place for it, if I had to shut up or whitewash my world, or otherwise alter it from what I've wanted it to be.
Of course I can't be perfectly authentic, but the truth of the matter is that I can't be perfectly authentic pretending to be anything other than myself. It's just not women I can't play with perfect authenticity. It's everything and everyone other than who I am. Am I any less authentic pretending to be a woman than I am pretending to be a jester with a ready wit and good humor? Am I less authentic pretending to be a dark skinned merchant buying cedar for the palace of a far off land, than I would be pretending to be an olive skinned slave boy working on the docks of that cosmopolitan market? It's all made up, yet I've never lived there or really experienced these lives. And there is no one that I can go to tell me what would be authentic, or what it is really like to live them. This is my world, it's all out of my head, and I am the only authority about what is authentic in it.
And the truth is, even to the extent that my world borrows liberally from ideas in the real world - as it must since my imagination is not limitless - there is still no one that can come to me and tell me what is authentic. Some woman can't come to me and tell me some character of mine isn't authentic, because just as I can't authentically be anyone but myself, they can't authentically say what is right and real for some other woman. And invariably an argument over who was or could be authentic would just degenerate down to averages, aggregates, and stereotypes of people - which wouldn't be authentic either. Now they might could say that my representation of women in the game was consistently disrespectful in some way, and though that has never happened, if it did happen I'd probably give it hard thought about whether I'm presenting a true diversity of female characters and or whether my female characters are the sort of characters that are respected or admirable in some way, or at least as admirable as the male characters. And maybe, depending on how strong of an argument they presented, I'd consider changing whatever element that person saw that had escaped my attention. I don't think that there is anything like that going on, and certainly my female players never brought anything like that to my attention, and granted when I had a sizable number of female players it was sort of like playing with the cast of "Big Bang Theory" so it wasn't a "representative sample of women" (whatever the heck that would mean). But sure, hypothetically speaking, there could be a deficit of respect in my play that needed addressing.
But this is not the same thing as saying I can't play a women because I can't play one real enough. I'm fairly sure that it is possible to pretend to be a woman well enough that you can't tell the difference over the internet, because I used to MUSH and it really was never possible to know anyone's gender and I've been mildly surprised both directions (guessing that a female character didn't have a female player, and being wrong, and guessing that a female character did have a female player, only to discover to my mild amusement that they were actually a male fire fighter in Alaska). If I can't guess, then the portrayal is convincing by at least one standard. But ultimately, that doesn't matter, since I can only really and fully be myself.
Since all of this has to be true of me as the DM, it would be hypocritical of me to hold the players to any different standards. I can't tell a player what to play, or that they aren't authentic enough to play that. So long as they seem to be respectful to the group, and taking their role seriously - which in my opinion includes avoiding jokey characters of all sorts, whether the jokes are offensive and not appropriate, or just would get old in a hurry, or would diminish the literary value of my game (or all three).
Like I said before, most RP is not to a high standard anyway. It's not like most tables are groups of method actors or aspiring thespians who bring consistent quality drama and characterization to the table. Most tables are trying to have fun without getting to deep into acting. Some players may be extremely shy and uncomfortable interacting socially period, much less getting into character. Some players may not enjoy dramatics. Many players just don't have the knack and really, regardless of what is on the sheet, are only playing themselves. And all that is fine, and in my opinion in good fun.
I mean fundamentally, if men can't play women in role-playing games, where are we stuck at? I mean forget that we lose something comparatively trivial, like the ability to play a RPG. If fundamentally we can't walk that far in another person's mocassins even as a leisure activity, how are we ever to exercise empathy and compassion for each other when its challenging?
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