I do not think bias is always bad. People use it for an excuse to do bad things, but having an opinion before hearing certain matters is not in itself all that bad.
I know that we have rescued a significant number of animals, and gave life-long homes to them, or found life-long homes for them. Most any shelter will necessarily have to kill animals, refuse to take more, or simply shutdown for lack of an ability to expand.
However, once we find an animal we can save, we do not shirk responsibility till we have someone else to accept that responsibility. Rewarding, but it can get expensive. Comical and, sometimes, amazing stories to tell...