BBC Radio 1 has said it will stand by its ban on the word "faggot" from the Pogues' 1987 Christmas hit Fairytale of New York to avoid offence.
The word, sung by the late Kirsty MacColl as she trades insults with Shane MacGowan, has been dubbed out.
But MacColl's mother, Jean, called the ban "too ridiculous", while the Pogues said they found it "amusing".
The BBC said: "We are playing an edited version because some members of the audience might find it offensive."
A Radio 1 spokeswoman said the station's management had met on Tuesday morning to discuss the issue.
She said they "had made their decision" and would not be going back on it.
The song is a duet between MacColl and Shane MacGowan
But the ban does not apply across the BBC. Radio 2 said it would be playing the full version of the track.
MacColl, who was killed by a speedboat off the coast of Mexico in 2000, brands Pogues frontman Shane MacGowan "you scumbag, you maggot, you cheap lousy faggot" in the song, which reached number two when it was first released.
She continues: "Happy Christmas your arse, I pray God it's our last."
Another line, where MacGowan calls MacColl "an old slut on junk", has also been edited.
Jean MacColl told BBC Radio 5 Live's Breakfast: "These are a couple of characters - not in the first flush of youth, I would have thought.
"This is the way they spoke. Today we have a lot of a gratuitous vulgarity and whatever from people all over which I think is quite unnecessary.
"They are what they are. These are characters and they speak like that."
A spokesman for the Pogues, who first formed in 1982 and reunited in 2001 after a five-year break, said they "found it amusing that a song that has been one of the best-loved Christmas tunes should suddenly have been deemed offensive".
Listeners have also been criticising the ban on the Radio 1 Newsbeat website.
Denise Venn said it was "a complete over-reaction" and Simon from Southampton called it "political correctness gone mad".
Dean in Southampton added: "I'm gay and it certainly doesn't offend me.
"I find it more offensive that the BBC has tampered with this track which hopefully will be number one this Christmas."
However, veteran gay rights activist Peter Tatchell said Radio 1's actions were right.
"The word faggot is being sung as an insult, alongside scumbag and maggot. In this abusive context it is unacceptable," he said.
"It is shameful that BBC Radio 2 and other radio and TV stations are continuing to play the full version with the word faggot included. It shows that they don't take homophobic language as seriously as racist language."