What does the term "moral complacency" mean?
Moral complacency describes an unwillingness to examine one's moral opinions as fallible; it is the belief that one cannot be mistaken in one's moral precepts. People who are morally complacent often believe that there is such a thing as moral truth rather than moral opinion. Morals can vary depending on one's culture, one's upbringing, one's religious belief, or even one's own attitudes and knowledge: this is the concept of moral relativism. The idea that one's own moral opinions are actually a kind of moral truth can lead one to the conclusion that others's moral codes are objectively wrong, and this can make compromises or diplomacy difficult. Complacency in general is not typically considered to be a positive quality, and it is certainly possible to see its dangers here.
Moral complacency is a term that refers to people rejecting moral opinions that go counter to their own as a moral opinion is one that is considered as the absolute truth of sorts and about which one cannot be wrong. It is a belief that a moral opinion requires no justification and as a result the issue of proving or justifying it and be willing to change the way one thinks based on better arguments presented by others does not arise.
As an example, if you believe that abortion is wrong, you may consider it totally justified to not hear any argument of mine to prove that abortion has its benefits, that abortion is not putting an end to a life, and the alike.