Used to express disapproval of someone's self-important attitude, not just moral strictness. Stop being such a prig; everyone's entitled to their own opinions.
Pro Tip 2/3
Often Insulting
Usually meant as an insult, implying annoyance with the person's behavior or attitude. He dismissed their advice with a priggish scoff, as if he knew better.
Pro Tip 3/3
Cultural Nuance
Recognize cultural viewpoints when calling someone a prig, as ideas of moral superiority vary. In a laid-back culture, calling someone a prig might be particularly offensive.