In my personal opinion, the first and most important thing to know is that being a furry is like being a gamer:
Some just browse some news or visit a forum every now and then, some write articles and write fiction/do artworks, some make it a living, and some submerge themselves completely.
Sometimes things go wrong (such as when a mentally disturbed person ends up on a killing spree), and ignorant people blame their hobbies when it's really the fact that when a large group gathers, there will always be some odd ones in the mix. It doesn't mean that every gamer is a serial killer.
Once they accept this, then you're pretty much safe.
From my experience.