On all my favourite polos and tees, I fabric glued another layer of stiffer cloth in a whole strip where the breasts reside and around the back too.
It looks like it was designed that way and keeps my nipples from showing.
I also experimented with light spritz of acrylic clear coat inside, same as before, the whole strip including the back.
Works too but use on finer fabrics. Coated honeycomb type fabrics = abrasion hell
My less extreme alternative was wearing double breast pocket shirts, but have been repeatedly told to get some "style"