Bucks may develop dewlaps; they are basically fat deposits. There are some breeds where a dewlap on either sex is a DQ, and some where it isn't mentioned in the breed standard at all (and one may assume is not an issue, either for bucks or does). The standard for the New Zealand says that a small dewlap is permitted on does; I'd be willing to bet that trying to keep that dewlap small could be an issue in an older doe. If I was thinking about showing, I wouldn't keep a young buck that had a dewlap, but an older animal that may be a bit soft all over? I don't think I'd rule him out strictly because of that.
I won't say absolutely get these guys under ground or onto the dinner table because of the respiratory problem; I will tell you about a little experience that I had. I had bred Harlequins for several years, they are a rather rare and difficult breed, so finding good ones isn't easy. I had made arrangements to have a family member pick up three animals from a breeder that lives several hours away from me. I don't know if the stress of travel caused the outbreak or what, but by the time I saw the rabbits, they were sneezing (the breeder insisted that they hadn't been doing that at home, and having known her for years, I have no reason not to believe her). I kept them well away from the rest of my herd. One, a doe, had been accidentally bred; she kindled a litter that started sneezing while in the nest. They were all culled - no survivors.
The two bucks I kept separated, but did use for breeding. The does were allowed in the bucks' cages for no more than a few minutes; if a doe didn't breed right away, she was quickly removed. None of the does exposed in this manner ever developed active snuffles, nor did any of their offspring. The bucks had pretty much cleared up on their own, though - I only heard occasional sneezes from them, and never at a time when I had a doe in with them. I knew I was taking a risk, but it was a calculated one (new blood of any kind was hard to come by, and these animals were otherwise pretty good). As I think has been stated, most rabbits have been exposed to the bacteria that can cause snuffles, and probably carry the bacteria with them, but their immune systems are robust enough to keep the bacteria in check. Part of the logic of culling symptomatic animals is to remove those with weak immune systems, thereby keeping the genes for better immune function in your herd. I guess the questions should be, how difficult are these animals to replace? Can you continue to keep them separate from the rest of your herd, and what will you do if the others start sneezing? This may not be an issue of an aggressive bacterium, it may be a matter of inadequate resistance; can you afford to risk keeping that in your herd?
