I hope this post isn't too controversial. I have a couple of white bras that I got recently because the weather is going to be in the upper 90s in the foreseeable future, and if white does the best job at keeping out heat, then so be it, but people get all puffed up if they can sense a white bra under a shirt. White apparently is more visible under certain colored shirts, than are nude or black bras. I have nude/black bras too but I'd like to have one more practical color. I'm more worried about the color of the band getting dingy over time, honestly.
Aside from the color of the bra, I think that people get too upset over seeing bra lines under shirts or bra straps unwittingly sticking out from the shoulder of a shirt. My intent isn't to make people lust after me. It's just that...a bra is a garment, it has edges, it has straps and well, those things show at times and a part of me wished I it mattered more to me, but I think to myself, the people who get so offended by it must be watching porn at home and hence have no right to be offended. I don't know. If it's a work setting then we probably have to obey them (cringe) but other than that, I wish I cared, but I don't think I do.
I am a large breasted woman and I don't wear a bra in general. (Working out and job interviews are exceptions to this). What I have found is that after the initial couple of weeks when my muscles were readjusting, my back pain decreased. So I am going out and about in my daily life with my large boobs jiggling about.
Most people don't care. A lot of the judgement is internalised, and yes, some people will care. They have always been rubbish people though whose opinions I don't care for.
It's not quite the same as your problem, but I think the underlying issue of woman's bodily autonomy is the same.
I do live in Britain, so perhaps the culture is different where you are?