The abandonment or renunciation of a religious or political belief. "the execution of their leader for apostasy brought widespread criticism"
Wikipedia - Belief Bias is the tendency to judge the strength of arguments based on the plausibility of their conclusion rather than how strongly they support that conclusion. A person is more likely to accept an argument that supports a conclusion that aligns with his values, beliefs and prior knowledge, while rejecting counter arguments to the conclusion.
noun - The state of having inconsistent thoughts, beliefs, or attitudes, especially as relating to behavioral decisions and attitude change.
Wikipedia - In the field of psychology, cognitive dissonance is the mental discomfort (psychologial stress) experienced by a person who holds two or more contradictory beliefs, ideas, or values. This discomfort is triggered by a situation in which a person's belief clashes with new evidence perceived by the person. When confronted with facts that contradict beliefs, ideas, and values, people will try to find a way to resolve the contradiction to reduce their discomfort.