To be dogmatic is to follow a set of rules no matter what. The rules might be religious, philosophical, or made-up, but dogmatic people would never waver in their beliefs so don’t even think of trying to change their minds.
Dogmatic goes back to the Greek words dogma, which means basically “what one thinks is true” and dogmatikos, “pertaining to doctrine.” To be dogmatic is to follow a doctrine relating to morals and faith, a set of beliefs that is passed down and never questioned. It also refers to arrogant opinions based on unproven theories or even despite facts. Someone dogmatic might insist that dinosaurs never existed or that women shouldn’t drive. Dogmatic people are usually not very popular.