Misconception. Homosexuality has, as far as academia can tell, never been more or less prevalent throughout humanity at any period of our cultural development. There were likely as many people with non-hetero orientations or gender dysmorphia as there are today. The fact is that a more accepting culture causes people to be more aware of (the thing the culture accepts) so it appears as if it's a new or growing phenomenon. Consider the Greeks, for example. The lesbian poet Sappho, the homoerotic art and religion, the prevalence of mentor/apprentice relationships - and things like that are present throughout all history. Of course, we know less about it in the medieval period since it was strictly covered up (although 'sodomites' weren't executed or persecuted nearly as often as you may think, it was mostly just a shameful thing you didn't admit to. Like STDs!) but look for the history and you will find examples of it. So no, homosexuality was as 'common' as it is today, only about 3 or 4 percent of the population (in the US).
Anyway, my issue with genderbenders is thus. And for the record, I have played several male characters (usually they're big husky guys because it's different from a feminine stature, change of pace, etc etc) and many characters with orientations other than my own. The problem with portraying someone of a different sex, gender, race, sexuality than you is that stereotypes are drilled into your head and skews your portrayal of a person, and often they're turned into your tokens or your strawmen. I don't mean to say that anyone who is not a purple alien from Pluto can't possibly understand what a purple alien from Pluto is really like. I mean that people don't put in the effort to understand - or rather, not to try and understand, but to forget their misconceptions.
Take the guy who said that females are better to play kinder, maternal roles. There's a difference between a female character being a healer and all your healers being female characters. To "genderbend properly" (I sound pretentious bear with me) you have to realize that your character's sex only truly matters when it is directly affected by the conditions of the world around them, and not who they are as people. A poor genderbender isn't exactly the strawman lesbian-bimbo-snowflake that other commenters have argued against, but one that misrepresents and misunderstands an entire sex/gender/ethnicity/sexuality because they fundamentally believe that that certain aspect affects the rest of their character's personality.