I do find it odd that it's fine for men to walk around in T-shirts tight enough to see their nipples is normal, but women doing it must be attention seeking and worthy of derision
I don't view it as a social faux pas, but - as someone who hasn't worn a bra since a few months after I left home as a teenager, decades ago - I think it comes down more to what you wear without a bra than not wearing a bra itself unless you're big enough that it's going to be obvious regardless. Not wearing a bra can mean dressing differently to a lot of feminine fashions particularly if you're in a part of the UK where it's negatively associated to be obviously braless. Knowing what kind of clothes work well and don't without a bra is part of it, just like other discussed clothes that aren't great with certain kinds of bras.
I just don't like the feeling of anything snug on my torso. I wear loose clothing, typically in layers, mostly in dark colours, and I check clothes carefully before I buy them to ensure that the fabric isn't too thin. Even the few tank tops I own are loose with a thick material and I always pair them with an overshirt that has a thick material as well. While I don't like the heat, I'm not as bothered by it as some people and prefer not to have sun directly on my skin (I find that way hotter than wearing loose layers). I typically dress in a way that I'm 90-95% covered, only my hands, face, and some of my neck is visible most of the time, and I only wear loose, near-ankle length skirts. I view my style as more protective than attention seeking, and I may be oblivious, but I've never noticed a double take.
I work in an environment where dark suits are part of the norm, and I always wear a suit jacket - I think I can count on one hand the times I've removed my jacket in the office, and I only did so for at most 20 minutes while wearing dress that is at least double layered, thick, and black and doing something active enough that the jacket was getting in the way and the activity was making me too hot. Some of my coworkers, particularly in this heat, have worn lovely thin dresses that look great on them and I would not wear those dresses because they look quite snug and I know it wouldn't work well without a bra.
I only started to wear a bra at 12 because of my mother's insistence and she isn't around to complain at me not fitting into her ideals anymore. Luckily, none of my teenagers have ever seemed bothered about my style, and only one of my two daughters wears a bra. We're all on the small side, the one who wears them is probably the largest out of the three of us, likes to wear snug dresses, and doesn't like the feeling of skin folding over other skin, I'm small enough that I don't experience that unless I'm very hunched over even as a middle-age woman. My other daughter who doesn't wear a bra is the smallest in the chest of the three of us, hates most human attention, dresses androgynously butch, loose t-shirts and cargo trousers with a hoodie when weather allows are her favourite, often covered in mud, and works as a farm hand - the only male attention she wants is from her pet rats.