I suppose this would be a good point to say I'm interested in advice from anyone who has successfully converted a friend or family member's opinion of the site from knee-jerk negative to neutral or positive, given that I spent most of yesterday fuming about something absolutely ridiculous and insulting that was said in response to me bringing up the topic of cryonics.

Forget about what they think of a website. Who cares? The task is to train them out of thinking it is ok to say ridiculously insulting things to you at all! You're worth more than that!