I'm going to diverge from the prevailing YLF opinion and say that I don't think
you're off the mark in choosing to dress more conservatively for work than you would during your personal time.
It's essential to know what's appropriate for YOUR workplace, not somebody else's.
I haven't seen the Gap sweater in person yet, but I would approach mesh with extreme caution at work. If the weave is tight and looks more texture-y than hole-y (I hope that makes sense), I'd consider it. But I'd save it for a day when I don't have meetings with the higher-ups. And definitely make sure all bra straps are concealed!
(For whatever it's worth, sleeveless tops are not okay in my particular office. I wear them under jackets and cardis, of course, but the outer layer doesn't get removed unless I'm out of the building for lunch, walking to my car, etc.)
I know this isn't a popular opinion on YLF, but in most offices, it's useful to exercise some restraint unless you've reached a point in your career when you can get away with doing your own thing without repercussions. (e.g., Hillary Clinton) That doesn't mean your clothing should be frumpy and plain and you can't express yourself whatsoever, but you do need to think carefully about what image your clothing projects. And mesh, which can *hint* at skin that's normally covered, even if it doesn't actually reveal it, may not be a great choice for work wear.
Again, just my opinion. My age (32) and gender influence my thinking on this issue. I regularly get compliments from my bosses on how I know how to dress appropriately and still look fashionable. I don't have many peers who toe the line in terms of appropriateness, but those who do are not viewed in a flattering light by the powers that be. My rule of thumb is that if I'd be embarrassed to wear it in a meeting with the head boss, I probably shouldn't do it.