That’s what dress shields are for. (I don’t want to link to ads because they all feature bra-clad women.)
I would never wear a wife-beater under a white dress shirt, because you can see it, and it looks ridiculous.
Party pooper 
I wonder if part of the purpose is to prevent nipple-chafing, especially with starched shirts.
I too wear short-sleeve t-shirts, for armpit-sweat absorption.
They are a the logical result of warm weather working. If guys are working hard, it is warm and they must wear shirts, lots of guys would rip the sleeves off of t-shirts in order to keep cool. Someone had the bright idea of actually making shirts with the sleeves already off.
I wear them all summer long. As long as they are clean, un-torn, etc, they are fine. Also avoid the farmer tan.
That’s OK.
I’ve located the ads, but only because it will be a sad day for these forums when a fear of prurience forms a barrier to the acquisition of knowledge.
Don’t worry, it’s okay as long as you have one of those big gold medallions.
I never used to wear any sort of undershirt until I got my concealed carry permit.
Now I wear the sleeveless tucked in with the holster inside my waistband outside the t-shirt.
Then my normal shirt draped over it.
Protects me from rubbing against the grip and vice-versa.
I wear them for two reasons.
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because my nipples are always hard and it’s embarrassing to be a guy walking around with pokies all day long.
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I am fairly thin but have a little extra beer weight in my belly and chest. the tightness of the wifebeater smooths it out so my man boobs look less round like man boobs and more flat like a bit of muscle. Deceptive I know and it’s not perfect but it works to an extent. As far as the belly goes, the wifebeater does nothing for that, still have to suck it in.
Maybe I live in my own little PC world (too much, I’m sure,) but do people actually go around calling them “wifebeaters?” I haven’t heard the term aloud since the early eighties. I just call them tank tops.
Yes, people commonly call them wifebeaters. A tank top is the same general shape, but not the same thing because wifebeaters are ribbed and men’s tank tops usually aren’t. Women’s tank tops often are ribbed, though, oddly enough.
It’s a public service thing. You see, the shirt gives the police a convenient hand-hold when they wrestle you to the ground in front of your singlewide. Don’t you people watch Cops?
Maybe you think it’s tacky to show chest hair when clothed, but I find it erotic especially guys that can flaunt it when wearing a turtle neck. 
They’re called singlets here. I wear them all year round. They keep me warmer during the colder months and absorb sweat during summer.
I’m a woman, and I often wear tank tops as an underlayer in cold weather. This is usually preferable to a t-shirt, as wearing a short-sleeved shirt inside a shirt or sweater with long, fitted sleeves can lead to uncomfortable and unsightly bunching up around the shoulders.
In really cold weather I have sometimes worn a sweater over a t-shirt over a tank top to protect the sweater from…sweat…while not further complicating things in the shoulder area.
A tank top or camisole is also much better than a t-shirt under a sheer or light-colored blouse. The t-shirt sleeves would be obvious through the thinner fabric of the blouse.
Im a man. I wear them so my nipples don’t get rubbed raw.
I’d wear them in a warm climate where I had to wear dress shirts. But I don’t, so I don’t. Woven dress shirts just don’t feel right on the bare skin of my torso, and I’ve gotten chaffed nipples before. A soft knitted cotton against my skin feels better.
I think the tank top has more coverage around the arms, especially in the back.
My mom refers to it as a strapper tee, which for some reason always makes us giggle.
They are also a bit longer and form fitting than regular tshirts and so better for tucking in under a dress shirt.
Plus, they have a sort of ‘macho mystique’ to them.
I wear 'em because I just sweat. A small amount of dampness under the pits is a drastic improvement over an entire soaked shirt.