R’ Ovadiah Yosef (certainly qualifying as at least a daas yochid even for Ashkenazim!) is meikel altogether with ‘transporting nigunnim’ as Avi K quoted above.
We’re not discussing transporting stam secular music, we’re discussing avoda zara.
It is arguable that even R’ Moshe would agree in this case that its ok–not only because some Jews came along and translated the words into Hebrew with the problematic line being left out, but more significantly because even in the world at large, this song–i.e. the tune and general words–seems to be primarily associated with non-inherently-avodah-zarah-groups
The whole theme is avoda zara, and changing one line doesn’t affect that.
Rav Moshe writes that even if they no longer sing it, it remains assur, so whatever association people make won’t change the fact that it’s assur.