So is it more polite to get out / tune your instrument, rustle through your folder,and consult the other members of your group while others are singing?

No, of course not, but you can do it in the short gaps between the end of one song/tune and the next (assuming there is one, for applause, etc. - but I know not all singarounds operate that way). I get my guitar or other instruments out at the start and tune them then, and I would have a rough idea of what songs to sing beforehand. If I change my mind for any reason (e.g. someone else does a song I was planning to do - this did happen once!), I do usually have a song folder with me, which I can (quietly) refer to while others are performing, without disturbing others (I wouldn't do it while people sitting next to me are performing, though).

If you arrive late and can't get ready in advance, you could at least get the guitar (say) out of its case (quietly). I made the remark because I've been to singarounds where people wait until told it's their turn (when they know in advance!) and then get the guitar out, tune it, leaf through the music, etc. Then they put the guitar back in the case, and repeat this when it's their next turn. It's boring for the others, who have to sit and watch this 'performance', before the guy even starts. And it's especially annoying when there's not long to go, and you're wondering if you'll get another turn!