I note that most posters in this thread, including the OP, are referring to gender (cultural categories) rather than sex (biological categories). So let's go with that.
What gender categories mean -- what attributes or social roles are considered masculine or feminine -- depend on the culture. Another cultural variable, closely related, is how men and women are treated. A lot of gamers like their gameworld to mirror their real-world culture, which in my part of the world is unusually egalitarian. In most societies, past and present, gender is much more determinative of a person's social roles than in contemporary North America. How determinative is it in your campaign?
D&D is inspired my a melange of settings, some historic and some fantasy. In all the historic cases, and most of the fantasy cases, PC-type roles are men's work. Which doesn't mean that you don't find women in them, just that women aren't the norm. The treatment of a woman who chooses to don armour and go hunt monsters can vary from the scandalous ("don't let a lady turn out that way!") to remarkable (think of how Joan of Arc's mystique was partly due to the oddity of her femininity).
I like campaign world's to mirror this, because it makes gender a more meaningful character attribute, a more substantial part of the character concept. It provides options for character backstories: perhaps she became an adventurer, working on the margins of civilized society, to escape the uninspiring roles that her culture assigned her. It can affect social encounters: what happens if the people the adventurers have to deal with do not accept a woman in that role? Or, to go the opposite way, if she does achieve renown, there's a Joan of Arc dimension to her celebrity.
If you go this way, I'm strongly opposed to restricting character gender or sex according to player gender or sex. If a character concept fits your game, then all players should have the same option to play it. Why shouldn't I be allowed to play a character based on Joan of Arc, or my sister one based on Conan? Count we with the "neither encourage nor discourage" camp.
I'd say about two-thirds of my characters are male. But that's not because I'm male. It's because I think of male as the default for adventurers. A paladin who is female is a female paladin, while a paladin who is male is simply a paladin, sex/gender unremarkable. I like female PCs to be the exception. But I also like them to exist, and from time to time I want to play one, just because I like to try the full range of options. I've made characters of all races, all classes, all alignments, why not both genders?