As someone whose stock in trade has long been singing unusual (or obscure) songs, I can only say that my only objections to others singing them are
a: If someone sings it just before my turn comes up, and it's the song I was planning to sing, and

b: If they screw up the words on a song that I think was particularly well constructed.

I addressed the latter objection, as well as I could, by starting the Digital Tradition. Dunno what to do about the former one, except to expand my repertoire.