They can't seem to see past the fucking in fursuits/animal porn thing and they think that's the entire fandom, and chances are if I said anything they would ragefest at me for the rest of my life.
Better than "They believe the media lies", worse than "They know how the fandom actually is." There is a lot
of mature works put into the Furry Fandom, and multiple suppliers for assorted either Sex-Fursuit or Animal-Shaped Dildo toys. Some of which are advertised on FA's pages. Let alone sites which have features like "Cum Counters".
Essentially: You can't fault them for seeing it as a fetish more than a fandom. While it is a fandom, most discussion tends to boil down more to either wank-material or whose fursona is best.
As for the "ragefest at you for the rest of your life", that depends: Would you an hero for being mocked? Would you throw a major shit-fit for every mockery? If - at worst - they see it as nothing more than a dark fetish, they're just going to mock you now and then. Furs are infamous for over-inflating family reaction as opposed to their own action, for instance turning a family going "WTF?!" for finding a gig of Furry Porn on their computer into "SO I SAY I WUZ A FUR AND MY MOM CALLED ME A DISGUSTING FUCK AND MADE ME DELETE MY PICTURES IT WASN'T EVEN A LOT". For this part: Pardon me if I feel you're heavily inflating how badly your family / siblings will react. Heck, we've seen people in this thread
talking about how they told friends who are "Yiff in hell furfags" about how they're furries, and the most they seem to suffer is what I described above (The occasional mocking).