Meant to file this earlier... when I tried refusing the Rainbow Road quest (collect 30 coins), I was able to refuse it, but it prompted me for it again not 30 seconds later — and again, and again, and again, until I not only accepted it, but completed it successfully (when I failed it, it prompted me almost immediately upon returning to the zone I'd left). Given that the quest conversation also locks the screen entirely, it makes it nearly impossible to do anything else when you get a quest prompt you don't want to take.