Peri, I feel like the teal version is a little bit sheer -- I think I'm OK with the degree of see-through-ness (I'll experiment with whether a dark or nude bra seems to mitigate the issue), but I'll report more later. The red one, strangely enough, does not feel sheer. I tried on the black and white version, which didn't seem sheer either, and I liked it, but I would have preferred it more if the stripes on the pocket matched up with the stripes on the body, rather than perpendicular. Nitpicky, I know, but I have had my eye on a possible black and white stripe tee at Nordstrom (it would be a duplicate of a favorite mint stripe Splendid tee I have) -- I've included it from my Finds. Mine fits looser than the model photo.
But anyway, long response to the sheer question. I think my short answer would be, it seems to vary from one color to the next. You may have to try a couple to see how they look.
I have trouble with wide/deep necklines showing my bra too, and I always attributed it to my short torso! I simply measure short from shoulder to bust, so many necklines are too deep on me. It's an easy fix if it's a sleeveless top -- just take up the shoulders -- but not so easy in a sleeved garment.
Thankfully, these tees are not cut too low or wide at all -- they seem to stay in place well. I think it helps that there's not a deep back -- deep cut back necklines often cause me trouble, even though I think they can look nice.