My Boyfriend wears white ones once in a while, but not if he's trying to dress up and look good. He'll leave one on if we run to the store or have to step out of the house to grab something, and he usually wears them under his button ups or plaid shirts. I don't really think they are 'still in', but I don't think it's completely unacceptable to wear them.
A crew neck shirt is better than a v-neck shirt. That just screams douche. If you're wanting to dress up, of course a shirt with a collar is always appropriate, since time immemorial. But you should wear what makes YOU comfortable. Not what you think other people say you should wear, or what people say is "in style". A classic, simple, clean look will ALWAYS be in style. Don't jump on the trend bandwagon and you'll be good. Dress for your body type and you'll also be good. Just be comfortable!
Remember the goal of clothing isn't to look good on its own, its to make you look good. Crew neck tees have no structure. If they fit well and you have a good body, they show it off. If you don't have a good body, they're actually a bad choice compared to something with a collar or something that has a little more structure.