Hope you don't mind if I jump in here. In the early eighties, my childhood skin allergies kicked in big time, and I hated wearing a bra because I couldn't find a single one that was 100% cotton--the only fabric I could wear back then.
When I moved away from my parents, I stopped wearing bras altogether. They made my skin break out worse. So I usually wore colorful cotton t-shirts, the equivalent of a Hanes Beefy-T, with pictures and messages on them. Being young, I was...well, my chesticles were firm and high-set. They jiggled. Men liked them. I had mixed feelings about them, but I was in my assimilate-as-a-girl period, and I really had no choice about skipping the bra. Anyway, I liked men and liked the male attention.
Here's the thing. Maybe times have changed, but back then, I was treated differently because I was "loose." A lot of people thought that made me "loose," if you know what I mean.
I wasn't big--B cup--but men talked to my chest (that happens a fair bit anyway), some men thought I was easy (I was polyamorous, but not easy), and I got a number of requests that I pose nude for photos and sketches. Often, even when I was trying hard to fit in as a female, I was embarrassed.
Some female coworkers refused to even talk to me. I was close with a male coworker, and he explained that they talked about me behind my back. They thought I was showing off what I had, and they thought I must be looking to sleep around--or actually sleeping around. All because I didn't wear a bra.
My male coworker thought they were just jealous. I think it was a bit more complicated than that. People had been trained to disapprove of a braless woman.
I hope times have changed, but I suspect that a lot of people will still make snap judgments about a woman who doesn't wear a bra.