Sensitivity to others’ needs is good, but living life with good will is better. We should try not to give offense, but also accept that people make mistakes. If we do not forgive, we will not be forgiven.
Since you cannot have a discussion without first defining what you are talking about, let’s begin with definitions:
Merriam Webster online suggests that Political Correctness means “conforming to a belief that language and practices which could offend political sensibilities (as in matters of sex or race) should be eliminated.”
Wikipedia suggests that “Cross cultural sensitivity is the quality of being aware and accepting of other cultures. This is important because what is acceptable in some countries can be rude or derogatory in others.”