Depends on how you define the problem with a “Goyish” song. If the question is simply one of content, it should be fine (like Sukkas Ganba”ch). If it’s a question of Kadusha, even Gadol Omeid Al Gabov wouldn’t help (similar to Kesivas Sefer Torah, et al).
So, probably a Machlokes between the Litvish and the Chassidim.