The point I've been trying to make here, and fairly unsuccessfully I think, is that it behooves the player to play the character in such a way that these things aren't forgotten in play. If you choose something for your character, take a moment to think about how this impacts how the character will be played and make at least a bit of an attempt to convey that in play.
You've been unsuccessful because that isn't much like what you said at the start of this.
Your initial statement was that nobody at the table should ever have to ask what gender your character is. This is a very far distance from saying that your play should be plausibly in line with the background story of your character.
The former comes across as, "Hey, folks, like I tell you at the beginning of each session, my character wears a dress and has breasts! Remember I'm playing a WOMAN!" The latter may be more internally noting that you're playing a woman, and in her culture that makes her subject to certain forms of harassment, and your character will have zero patience for the guys in the tavern who get handsy with the serving maids, leading to a tendency of starting bar fights.
Note that a man could decide he has no patience with people in the tavern who get handsy, too, or just have a tendency to start bar fights. They may come at the same basic behavior through different paths, so the end behavior doesn't unambiguously tell you the gender of the character, but either is still solid role-playing.
There may be a more basic question behind this - do you feel that everyone at the table should always know the motivations of your character? Because that, ultimately, is what role playing is - translating the motivations of the character into actions, right? Does this process need to be obvious to all other players, or should a player be allowed to only present the end results?
I submit that it is the latter. And, in general, what the player communicates to others at the table (GM and players alike) are the things that the player wants others to engage with. If the player wants their gender-related motivations to be internal, rather than as a point of engagement with others, then they can de-emphasize the fact they are of a particular gender. If they want an aspect to be a particular point for you to engage with, then they can put emphasis upon it.
As an example, we'll take the character my wife is playing in my 5e game. My wife is 5' 2" on a tall day, and while she's strong for her size, her build is slight. In the game, she's playing a 7' 2" dragonborn paladin with 18 strength, heavy armor, and an axe longer than the party gnome is tall. The fact of the character's physicality is mentioned repeatedly during play, pretty much every session, because my wife *wants* to make sure we don't think of her personal physicality - she wants to be able to loom over people in the game in ways she could never do in real life.
The fact that the character is also female? Largely irrelevant - while we refer to the character with the feminine pronoun, the point that she is a *she* doesn't enter into play with others. The culture around her is so predominantly mammalian that her traditional gender role is unknown to most of the people she meets. The intent is that they react to "big frelling lizard!" way more than they react to "woman", by my wife's choice.
