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

Solution 1:

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

Solution 2:

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.

Solution 3:

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.

Solution 4:

Clearly it's a Semmit (if you're Scottish)

Dictionary of the Scots Language:

SEMMIT, n. Also sem(m)et, se(a)mit, semmad (Cai.). A man's (or ‡woman's) undershirt or vest, usu. of wool or flannel

[Orig. doubtful. Phs. orig. the same word as Eng. samite, a fine silk cloth, or a garment of the same, phs. worn as an undergarment and thence extended in meaning to any garment worn next to the skin, but the semantic development is not clear. O.Sc. has semat, of a Roman tunic, 1456. Semmet is found as a form of samite in 18th c. Sc. (see A. H. Dunlop Anent Old Edb. (1890) 38.)]

OED:

Semmit, n. Pronunciation: Brit. /ˈsɛmɪt/, U.S. /ˈsɛmət/, Scottish /ˈsɛmɪt/ Forms: ME semat, 15 semitte, 18 semmit, semmet.

Sc. An under-shirt or vest.