One person's ignorance is another's enlightenment. You're going to have a long road ahead of you if you engage everyone who, by your own judgement, has been deemed ignorant. You will rarely change someone's mind with words anyway... actions are much more effective.
Nah, ignorance is pretty much just ignorance. Anyway, it's less about convincing that person and more about convincing others who might think the bullshit that person is slinging around sounds reasonable.
As for actions, does "flaming them to rubble" count?