You know, I wouldn't be surprised if there was a correlation between preferred perspective, and this sort of thing. I know it's not a perfect 1:1 anology (and it's probably more of a sliding scale than an "either/or" proposition,) but I've always seen playing primarily in first-person as similar to taking on the role of an actor in the game. The interface is a tool for emoting into the game world, in that case, so the fewer layers that would get in the way of getting "into character," the better. As more of a third-person sort of gamer, I've approached that viewpoint more as a director than an actor. Having that one level of "remove" from the action feels right to how I approach the concept of roleplaying a character - even playing a game in firs-person just feels like a psychic dissonance to my sensibilities.
Having that level of disconnect between myself and the character, it doesn't feel as... "weird" to roll a female character in an RPG. It's a character I've created and am directing, as opposed to me attempting to "inhabit" the avatar of a female character. So yeah, I think perspective probably has a strong correlation here.
Myself, I've played a number of female characters in other RPGs. I know with Fallout, it just seemed to makes sense, somehow. Going even back to Fallout 1, my "main" playthrough character has always focused on Speech, Intelligence, Charisma, usually either Science or Repair, etc. Often to the detriment of STR and END. Usually it's 3 STR and END for 8s in CHA, INT, and AGI. For some reason, it just always felt more of a feminine characterization. Obviously, that's stereotyping - but I just had more trouble coming up with a compelling male character with those stats (in my head) than a female. Like, if I was casting an action movie - I just couldn't think of anyone that would fit as a male; while a small-framed actress filling that role would more easily be seen as a strong female lead. It just seemed more compelling, somehow.
And it's not necessarily a six thing, with me. But of course: I don't always roll female characters, but when I do - I make sure they're totally hot.
I figure seeing a female character in a protagonist role can be rather compelling, especially when filling a role where a male protagonist would be more "same old, same old." Take Ripley in Aliens, for example. That could just as easily been a guy, but put Sigourney Weaver in that role, and the movie takes on a different dimension.
Anyway, with that third-person aspect, I don't generally find roleplaying a relationship with a male NPC to be innately awkward. Still, when romance is going to be one of the focal points in an RPG, I do tend to prefer to play as a male character (Mass Effect, for example - if I did roll a female Shepard, she'd probably end up romancing Liara.) I do recall my first time through Jade Empire, none of the male character models really did anything for me. But they had this one female preset with these amazing legs and a very short costume - it was hard to turn down. I ended up, almost by accident, finding my character in a relationship with a male NPC, and that time it did feel awkward.
So I suppose it has that potential. I've played through games with gay relationships before (both as male and female PCs,) and had female characters in games pursue romantic relations with male NPCs, and never felt odd about it. But with that one game, it just felt odd to me.
I'm not sure in Skyrim, what I'm going to play as. (With as big as the Elder Scrolls games are, I generally only ever make it through the one playthrough, so it's kind of an important decision in my case.) If I do decide to play as a female character, I'll probably pursue a "hetero" relationship - depending on the character I create, how the actual mechanics of a relationships work out in that game, and simply circumstance.
But really, I don't see as how it's all that strange of a concept. To me, I'm kind of an aspiring writer in the first place. I don't find it really any different than writing a story with a strong female lead in it.