Okay, so I just want to chip in with the perspective of someone who isn't allowed to be stealth. My rainman-like daughter will announce to most strangers that her mom is a man and her mom is a handsome man and her mom is transgender and transgender people deserve rights.
If I ask her to be on the down-low about it, she'll occasionally very loudly and awkwardly call me DAD, and she'll say it so often it sounds suspicious.
So it's not my breasts that are prohibiting stealth. I have small breasts. But I know what it's like to be passing with someone the first couple times you meet them, and then you show up and there are some anomalous details.
It's annoying for transness to suddenly take over the conversation when you aren't in the mood for it. It's annoying to know that some people will switch to "she" and maybe ask for your "real" name. It sucks to play educator with people who aren't close friends or family.
In my experience, word gets around fast. Even good-natured people tend to talk about it.
I don't do any scurrying, but I do live in an ancient world's fair hotel that was converted to apartments, and we have communal bathrooms. I come back from the shower wearing just a towel, which kinda makes me want to scurry. Hairy legs, tiny feet, boobs, no glasses so I can't tell who I'm passing in the hall, and I'm never sure how much it matters. Sometimes I want to explain to everybody, but who cares?