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The decades-old catchy song, recorded by such big names as Dean Martin, Ray Charles and Dolly Parton, recounts efforts of a man coaxing a woman to stay with him and overriding her objections.
The woman's lines say "I really can't stay" and "Say, what's in this drink," and his lines include "Beautiful what's your hurry" and "Baby don't hold out."
Radio station WDOK in Cleveland, Ohio, took the song out of its list of holiday music due to objections from listeners, Desiray McCray, an on-air radio host, told local media late last week.
"When the song was written in 1944, it was a different time, but now while reading it, it seems very manipulative and wrong," wrote Glenn Anderson, another on-air host, on the station's website.
"The world we live in is extra sensitive now, and people get easily offended, but in a world where #MeToo has finally given women the voice they deserve, the song has no place."
The #MeToo movement exploded on social media last year after accusations of sexual abuse were made public against Hollywood mogul Harvey Weinstein.
Untold numbers of women have spoken up around the world about sexual harassment and mistreatment, accusing top names in entertainment, government and business and altering attitudes and the treatment of women.
The Midwestern US radio station's decision drew a barrage of comments on social media, where many people wrote that it was taking #MeToo too far and that the lyrics were playful and harmless.
Urban Dictionary, an online site that defines slang and street euphemisms, has described the song as a "Christmas date rape song."
Some artists such as Lady Gaga have recorded the song but removed lyrics such as "what's in this drink."
The song was written by Frank Loesser, who also wrote the Broadway musical Guys and Dolls.
The radio station's management did not return calls seeking further detail and comment.