@DaasYochid Rav Moshe ZT”L seems to be referring to unaltered songs or recordings by an עכו׳ם. He’s certainly not assuring the music itself, but the song and lyrics which are sung for the purpose of Avoda Zora.
He is assuring even if the purpose of that specific performance is not for avoda zara. He talks about Acher, and presumably his kavana was not for avoda zara, but was not allowed to sing those songs.
And if you read the rest of the teshuva, it sounds like he was against pretty much all Jewish pop music, as a lot of Rabbonim were and still are.
That’s not what he is saying, and that’s totally a side point. He rejects that the issur of listening to music after the churban should be why Acher went off, and instead says he sang avoda zara songs.