This is a topic that I've personally found very interesting over the many years I've been playing World of Warcraft and MMOs/RPGs in general. I've never considered it strange to play the gender opposite who you are in real life. Most of my characters in games are women. I also play men, I have male alt characters in WoW, but the majority of my characters are women. My death knight is a man. My paladin is a woman. My priest is a woman. My warrior is a woman. My rogue, who is now my main character, is also a woman.
From time to time, if you play a character with a gender different from your own, you absolutely will encounter people who are shocked by that fact. There are people who will frown upon it or find it strange. However, in my experience, it's a minority. Why should it be strange? This is a video game. It's a fantasy world. Whether you're approaching the game as someone who is a roleplayer or someone who has no interest in such things, it still doesn't matter who, or what, you play. You can never play yourself in a game like this one. You're not an orc. You're not an elf. You're not a fire-slinging mage. You're not a shape-changing druid.
Even if you choose to play a relatively mundane thing like a human warrior of a gender that matches your own, that isn't you. You most likely are not a perfectly chiseled beefcake who is expertly skilled in every form of weaponry known to mankind. Such a person has never existed. There have been many highly skilled warriors and soldiers throughout human history, some who have forged legends through their bravery and skill, but you aren't going to find someone who can pick up a ridiculous two-handed sword that weighs just as much as they do and be able to expertly wield it ... to slay dragons. Yue Fei, William Wallace, Miyamoto Musashi, Khalid ibn al-Walid, Zenobia, Lagertha, Tomoe Gozen, and every other warrior of legend and renown from history, whether man or woman, had one thing in common -- none of them killed a dragon. Even those with stories of questionable basis in reality, such as the aforementioned Lagertha and her sometimes-husband Ragnar Lodbrok, didn't kill any dragons.
Taking all of that into consideration, why would it be such an issue whether or not you play your own gender? I'm a man that plays characters who are women. I don't feel that it reflects on my real world masculinity (or lack thereof) in any possible way.
Inevitably, this topic brings up a question: why would you play a character with a gender different from your own? The answer is simple. You play one because you want to do so. Why would you eat a hamburger for dinner? Because you want one. Why would you drink a glass of water? Because you want a glass of water. It's a choice with absolutely no serious ramifications on your life, nothing more than one small, irrelevant aspect of how you spend your leisure time.
Play whatever you want. It doesn't matter. If someone has a problem with that, that's not for you to worry about. The simple act of choosing what sort of character you want to play doesn't hurt anybody. Not playing what you want to play because you're worried about what others will think does hurt you and your enjoyment of the game.
To explain all of this more simply, I defer to an old adage coined by individuals far wiser than I: Haters gonna hate.