What is a less controversial name for the clothing item known as a "wife-beater" in the United States?

I've always heard them referred to as tank tops, or tanks.

Wife-beater may be regional slang; I never heard the term used while growing up in California.

I've always referred (and heard and read others referring) to them as A-shirts (as opposed to T-shirts). They're sold as A-shirts, too.

The shirt in the OP is not the best example of what people, at least originally, meant by "wifebeater".

Instead, "wifebeater" meant a finely ribbed, thin fabric, white, A-shirt, sold in multipacks as a men's undershirt like this.

For higher quality shirts like in the OP, say "tank top".

For a true "wifebeater" shirt, say "sleeveless undershirt". By "true" I mean:

See the 1998 article Teen Slang for Undershirts ("Wife-beaters") Causes Stir:

A "wife-beater"...is an old fashion, sleeveless undershirt... The "wife-beater" shirt isn't some nouveau tank top. It's the ribbed undershirt once worn only by granddads and Stanley Kowalski in A Street Car Named Desire

These were undershirts. Not just sleeveless but no shoulders either. T-shirts were also used as undershirts but carried their own specific name.