Avrom, I saw your comment in the other thread about this issue (and reference to my comments here.) I wanted to reiterate that the idea of making a song from this is only on the basis if you’re okay with songs such as shelo asani goy and songs from pesukim, brochos, parts of davening and from the Gemorah. If one in general opposes such songs, I would agree a song of shelo asani isha is to be opposed on that same basis.
But for those who buy the popular albums from the last 60 some years that are replete with songs of brochos and pesukim, then I don’t see a difference between making this into a song and making shelo asani goy into a song (as has been done on popular albums.)
The same intention when singing shelo asani goy at any random time of the day when not saying Birchas Hashachar, would be to thank Hashem for that purpose for that reason. For exactly the same reason Chazal included that brocha in Birchas Hashachar, and that’s your intention during Birchas Hashachar, so is your intention the same when singing it at other times. I don’t think the description of singing shelo asani goy due to “Jewish pride”, as you’ve suggested, is the most accurate description of why to sing it. It may be a partial description. But the bigger and more accurate reason to sing it ten times a day is because you are really thankful to Hashem for giving you that brocho, for the same reasons Chazal considered it a brocho that we should thank Hashem seven days a week for.
And so too with making shelo asani isha into a song. The reason to do so is to thank Hashem anytime of the day, any number of times, for this brocho we’re thankful for, for the same reasons Chazal incorporated this brocho into Birchas Hashachar for us to thank Hashem seven days a week for. No more, no less. You don’t even need any musical instruments or anything more than simply singing it from the heart. At a tish, at a farbrengen, at a kumzits, at a melave malka or at other times.
We could do the same about any of the brochos.