I'm sure neither words means someone who won't change his mind. According to an online dictionary faith is the belief in something without evidence, and dogma is a prescribed doctrine. So a Catholic has faith in the Vatican's dogma.

Not all people with faith refuse to listen to argument and to change their minds. It's possible that confronted with evidence that proves a belief wrong that someone who'd previously believed without evidence will change his mind. Even the Catholic church managed to give up its concept of a geocentric solar system when presented with enough evidence. Eventually.

However someone who believes things based on evidence is not going to be convinced by such arguments as "the Pope says it's true, so it must be", or "this old mistranslated book says it's true, so it must be".