So, putting it all out there, I'm transgender (MtF for those curious). I've lived my life under both roles and happen to be able to RP both genders rather successfully in my personal experience. I feel like my female characters are much more natural, never really sexualized, modest and honestly, other than a few tropes I use for definition, the gender of my characters could be swapped without changing anything vital about them.
But where does that leave me in this conversation? Technically, there's arguments saying that I'm "weird" no matter what I play, so a conversation like this puts myself and likely a few other members in a very peculiar situation.
@MonMarty has some good points, but I feel like fundamentally, it doesn't do justice to the actual reasoning why people lack the ability to RP certain genders: practice.
It doesn't matter if you're the most testosterone-fueled, heterosexual man, if you RP nothing but women, I would put a lot of money on the fact that your women are much better characters than your men. If you suck at RPing certain characters, it's because you don't have enough practice RPing those kinds of characters. Yes, it's true that your own person can help you fill certain roles easier, but more often than not, experienced roleplayers grow out of using themselves as a character analogue. This means that even male players playing male characters will take practice in developing characters different from themselves, almost as much as it takes to play a different gender in whole.
As far as the topic at hand, my advice is to stop looking at characters as their players. Period. That's the fundamental issue here that people don't seem to want to say. The reason people feel "weird" in the first place is because they're not using a proper RP mindset. They're not distancing themselves from their characters. They're trying to make their characters avatars of themselves and as such, can't see the forest for the trees. They see players, not characters. It doesn't matter what skin or name the person is using, the interaction is superficial at best because at the end of the day, they still feel like they're a player interacting with another player and not simply writing one side of a story between multiple characters.
In the words of Queen Elsa...