I think I would not be so nice to strays if I had livestock. I don't, but someday I might (I have always wanted that life) and you are right. You can't afford to wait until something happens. By then it's too late. I would probably at least try to find the friendly dogs homes, like I do now, but I would not tolerate the rest. There are just too many nice dogs out there for people to adopt. It's really too bad that people dump them, as many behavior problems are the owner's fault anyway. Some of those dogs never had a chance.
Our collie was dumped. She was pregnant and I guess they didn't want the puppies. She is wonderful and sweet. She was easier to take a chance with because of her breed, and we had a reasonable explanation as to why she had been dumped. Mixed breeds that are dumped are more likely to become a danger. I guess this also depends on the mix. I think I'd be willing to give something that appeared to have lab, terrior, or collie a chance. German shepperd mixes seem agressive, though it could be that they are mixed with pit bulls. Don't ask me why, but that seems to be a popular breed for non ranchers in these parts.