Dogmatism is a way of thinking that is stubborn and narrow-minded, often because of prejudice and bigotry.
This word has nothing to do with dogs. Rather, it has to do with being dogmatic: holding onto a view or set of views no matter what. The noun form is dogmatism, which is often a type of prejudice such as racism or sexism. Dogmatism includes a disregard for other people's opinions: there's no compromise possible.