I've only just accepted myself as a furry recently, so nobody knows anything about me. I mean my friend kinda notices how many furries I tend to draw (I made the excuse that I wanted to see if I could do it, since they're harder to draw than humans). I think he takes the majority view of furries being freaks, but then he would say anything if everyone else was saying it too. Frankly I don't know if I'm ever going to tell my family, but I will tell the friends who don't live near me and have never been to my house or met my family. I'll definitely tell my girlfriend, eventually. She's a freak so she'll probably understand.
As for why it's so hard for people to admit such a thing, I think it's because it's really very different. There's a leap between being an animal lover and actually being an animal. I mean people still think that anime is all extreme sex and violence or just for kids, and they think the same about games, and yet these things are so huge. They're far bigger than the furry fandom. I guess mostly it's the fear of the new. Furries only really became big recently.
That said, there's no guarantee that it'll all die down soon, since people still have the "Comic Book Geek" image embedded in their brains, despite comic books being around for so long, and spreading so far.