Don't show them anything that they don't trust. Show them their own litteratrash, and ask them to explain it while you practice a bit of shutup.
Don't pick a subject that impresses you, pick one that affects them, personally. Something that they said to you in the past. And don't start anything. Let them start, then steer the conversation to where you want it to be, ask your question, then shut up except to make them talk, stop them changing the subject and to keep them honest.
It is their job to defend their decision to stay with a failed doomsday cult, not your job to explain your decision to leave. Don't express your opinions, they don't want to hear them except to find an excuse to bash your character.
Repetition for emphasis:
Shut up
Make them do the talking