Three 1970s sources show that literal wife-beaters were already associated with wearing (just) undershirts by then.
Wife Beating: The Silent Crisis (1977) says:
Conventional wisdom depicts the wife beater as a lower class, beer-drinking, undershirt-wearing, Stanley Kowalski brute
New Woman (1978) says:
Conventional wisdom depicts the wife beater as a lower class, beer- drinking, undershirt-wearing brute
Wife Beating Law and Society Confront the Castle Door Gonzaga Law Reviews (1979) says:
Contrary to what many believe, wife beating is not confined to the poor, "beer-drinking, undershirt-wearing . . . brute."
So this stereotype was already solidly in place by the 1970s, well before the TV show "Cops".
In the 21 August 1995 article Fashion Ground Zero in New York Magazine, Dany Levy describes checking out the fashion of kids at Lollapolooza, and begins with:
Heidi, a stick-thin blonde who cites Archie Bunker as her biggest fashion influence, is wearing what she refers to as her "wife-beater tank," a simple Hanes job dramatically splattered with mud ("$4.99 at Woolworth," she asserts, sticking out her boobs)
It seems to me in this early example that the author is a little uncomfortable with the term, but since this is a girl or woman saying this about her own shirt, and this was 1995, it didn't easily imply a literal meaning.
There was a 23 June 1998 article Teen Slang for Undershirts ('Wife-beaters') Causes Stir about the term in the Sun Sentinel. So it was frowned upon to some degree.