I am getting more picky, but my tolerance for cigars that aren't great is still pretty high. I don't think I've had a cigar that I've ever stopped smoking because of taste. I've enjoyed each one but there are several that I've had that I won't buy again. However, if I'm in some situation where it comes down to smoking something that I know is just OK or not smoking at all I'll choose the former.
It's like with beer. If I go somewhere where they only have Bud Light I'll drink it and not have a problem with that (crappy beer is better than no beer), but I'd never choose it over a decent craft beer.