Hugh of Lincoln is one I've been thinking about recently. I bought the Marrow Bones/Southern Songster/Wanton Seed/Southern Harvest songbooks over Christmas and have been learning many songs from them.

I can't remember which book it's in, but there's a version of Little Sir Hugh in there, collected from a Hampshire singer, which has no references to Jewishness at all. So if someone were unaware of the song's wider history and they picked up that book and learned that version, for them that song would have no anti-semitic assosiations.
(Course, it'd still be a gruesome song about child murder)

That prompted me to look at other versions of the song. Almost all of them have two references to Jewishness - two lines, And both of them could very easily have the reference expunged.

For many singers, I think even a revised version of the song (or non-revised in the case of oral tradition versions that do not mention Jewishness) is still too tainted by association with anti-semitism. But it raises interesting questions on whether recuperability is possible or not.