My [F] coworker [F] shows up to work without a bra, is this appropriate?
I guess from a technical standpoint this is a question of your workplace's dress code. Is she supposed to be wearing a bra? Does it not specify?
Personally... I don't care. As long as you can get your job done I really don't care what you're wearing.
...her nipples are showing...
I don't know if this is really relevant or not, but just wearing a bra doesn't guarantee your nipples won't show. I'm a man and my nipples are pretty much always visible through a regular tshirt or polo. I have to wear thicker/heavier fabrics or undershirts or something to hide them.
This is an engineering firm with lots of men.
Now I'm going to go completely off-topic... But I find it interesting that you felt the need to mention this.
Does the presence of men change whether it's appropriate, or not, to go bra-less? Is her comfort trumped by their presence? Is it her responsibility not to be distracting? Are the men not responsible for themselves? Their own thoughts, actions, or distraction?
I don't really have good answers to any of this... It's obviously a somewhat complicated situation with different factors at play... But I do find it interesting how we typically put the burden on women to hide anything that could be "inappropriate", rather than making men act appropriate.