If you are a guitar player, and you really don't want anybody else to join in instrumentally on your songs, the politest and most effective way to prevent this is to tune your guitar down by exactly a quarter tone (if you have light gauge strings you could tune it up a quarter tone). Ideally, you would have a Snark tuner to accomplish this quickly and accurately, ( and obviously you would have done it before your turn to sing)

Ideally, you would also use a capo and an open tuning, and this will totally throw any unwanted would-be accompanists, who will spend the entire duration of the song trying to figure out what key you are actually playing in.   

Of course, if you are one of these unfortunate people cursed with so-called "perfect pitch", it might be difficult to sing a song a quarter tone below concert pitch, but I don't think that would be a
problem for most folk singers.