Since the word "prejudice" refers to an old and unpleasant idea, can I say "dogma" instead?
Unfortunately no. I don't think "dogma" would work here. Having a "prejudice" against someone or something means an unfair and/or an unreasonable opinion or feeling towards someone or something. "Prejudice" is about making a judgment on a person or people on their outward appearance. "Dogma" means a fixed belief or belief that others are expected to follow. "Dogma" is mainly paired with religious organizations or groups, such as how Christians are expected to follow and believe in the ten commandments and Jesus Christ. Emma uses "prejudice" in her speech because some men and some businesses have an unfair opinion on women, treat them differently, and want equal rights in the workplace.