What Douglass means by this is that a person cannot be truly bad in some circumstances and still remain good overall. A person who acts in evil ways in any part of their life will soon see their entire conscience fall apart and they will be evil in all parts of their life. This is, in a sense, a similar idea to that expressed by Martin Luther King, Jr. when he said that injustice anywhere is a threat to justice everywhere. Douglass is saying that injustice in one part of your conscience will eventually threaten all parts of your conscience.
We can see this from the context in which Douglass places this passage. He is telling the story of a woman who owned him. He says that the woman was, at first, a perfect Christian. But then, as she enforced the rules of slavery on Douglass, she lost her good nature. She came to be even worse to him in some ways than her husband, who had previously been worse than she was. Douglass is saying that accepting slavery eventually destroyed her conscience and allowed her to become a much worse person than she had been.
What Douglass is saying, then, is that we cannot compartmentalize our consciences. We cannot be evil towards some people and then turn around and be good to others. We may manage it for a little while, but not for long.