I agree; very often the character's gender is important, because there very well are differences in the genders. I added the addendum "so long as there aren't relevant features" for this reason. I feel the problem aries that we (in media, at least) tend to focus on the fact that there are differences, when by and large they aren't important in the day to day. If we're watching a film like an action film in a situation where it would be rare for a woman to exist, perhaps the American Civil War, and a woman was a character, it would absolutely be important to have the women and men distinguished and discussed, but when every film that has a woman focuses on the fact that she's a woman, that she's different because she's a woman, or they make mention of something that only happens to women, or they shoehorn in a romantic subplot because she's a woman interacting with men, it's absolutely exhausting and irrelevant. It's akin to if you make a film and have an Asian character, and they have to make mention of it somewhere regardless of its relevance-- he's just a character with the same depth and doing the same things the rest of the characters are, but making a point to make a distinction for superficial reasons is distracting and takes away a level of sovereignty the character has from who he is.

For example, if you take a work like Lord of the Rings and made Sam female instead, the work isn't affected. It remains identical and the he still has the depth of character, he's still just as much the protagonist. You could not change the gender of Eowyn, for example, because it's pivotal that she is a woman instead of a man. Or the same of Aragorn, because he is expressly the king of Gondor and a warrior in a time of male warriors (rightfully or not). The problem is, in these situations where someone is writing a female, they'll tend to fall into cliches. They'd have Sam fall in love with Frodo, or have her break down and question herself, or have her be flat and only have the characteristic of 'strong' and unchanging throughout. The dynamics of a person change dramatically when they are actively writing a female character, writing a woman™ instead of a person.

To add a summary, I'd say about 80% of the time gender is irrelevant, but writers make it relevant because they feel they have to as they're writing a female, even if it flattens the character and removes depth. They make far less interesting people in their stories when they do this, subconsciously.