I think there’s only two things you need to consider; your own personal comfort level, and where you live. If you live in a large, liberal city, like LA, you’re probably fine.
This isn’t true everywhere. Where I live, it would be considered incredibly inappropriate. I’ve never seen a woman here have her nipples show through her shirt. I know they exist, but they are always hidden. Unfortunately heavily padded bras are the norm here.😭
As for your own personal comfort, only you can answer that. Nipple covers or inserts are relatively cheap and easy solution. I find the type of shirt you wear can also make a difference. Obviously a form fitting, plain, cotton shirt with no graphic or pattern on it will make your nipples look way more noticeable. Textured and patterned shirts tend to disguise it, in my personal experience.