TL;DR answer: Being a breeder should not be automatic grounds for disallowing questions or answers. References to killing healthy animals will almost certainly detract from the quality of our content, and should be removed via edits and deletions. Questions specifically about killing healthy animals should not be considered on topic.
I've looked at the question you mentioned in chat, and I don't see anything in it that indicates that the rabbit in question might be killed or sold for medical testing. It looks like there was some comment discussion, and I'm guessing perhaps something was mentioned in comments that lead you to believe that those were possible outcomes?
If so, then I'm strongly in the camp of "No, we should not disallow questions from breeders simply because we believe they may not be treating 100% of the animals they breed with the love and respect pets deserve".
John Cavan hit the nail on the head: questions raised by breeders may have applicability to standard pet owners.
However, you are right that seeing content discussing deliberate killing of otherwise healthy animals is likely to be discouraging to visitors.
A unilateral ban on questions from breeders, even if only of a subset of breeders, is not the right solution to this.
Instead, I would suggest edits and/or comment cleanup as a solution for the majority of instances of this potential problem.
If a question indicates killing an animal as a kind of ultimatum (i.e. "If I can't resolve this, I'm going to have to put the animal to sleep"), then that portion of the question should be removed via edits (keep in mind this only pertains to questions about healthy animals). The potential fate of the animal if the question isn't resolved adds no value to the question, and may put off some people.
The only other scenario I could come up with would be a question asking specifically about ways of killing an animal. These can be legitimate questions, but to avoid unnecessary controversy, the questions should avoid mentioning that the reason for the euthanization is for commercial reasons, or other reasons unrelated to the animal's health and happiness. While this toes the line a bit close to censorship, I see no reason that the context is really necessary for these types of questions, and instead invites sidebar discussion and other undesirable noise. Edits should be made to maintain the relevant information, while removing any discussion of non-health-related motivations for euthanasia.