I think your use of the word ignorant is incorrect. Ignorant means "not knowing" and usually not a choice. If you choose to not know about something, you're an idiot or bigot or poilitician or fearmonger, etc. And once someone makes a choice to up hold an opinion without evidence, they're really saying you are not important.
So what do you do when someone dismisses you? You first must disagree. Then, you can either waste your time arguing or surround yourself with people who know how to think, discuss calmly and have a desire to learn about something they are not.