I usually relate better to people who like animals than those who don't.
My cat is my best friend, I've had many pets, much of my life has been spent on or around nature preserves, and I'm a nature lover in general. Fauna, flora, astronomy, you name it. Being a fan of science fiction and folklore, enjoying comics with animal characters, it's all pretty consistent for me. At a party, I'm the stereotypical introvert in the corner keeping the pets company... and maybe chilling with other people who like animals.
If you can help animals, that's awesome. Having pets can scratch that itch. There are other ways to become involved, of course, but a lot varies depending on where we are in life and what opportunities are available. I've thought about volunteering at local animal shelters, but I'm too squeamish about things like euthanasia and hearing how various pets surrendered to the shelter may have been mistreated. There are things I'd rather not know.
I'm not sure what a typical furry is. Some may just like the community or the aesthetics of the characters. From a design and social perspective, that's cool, but I wouldn't expect a typical furry fan to delve much into science or philosophy.
As I'm typing this reply, I'm thinking that part of what appeals to me about these characters may be that (in my mind's eye) they represent fellow people like me who like animals. Kind of gives another layer of meaning to what some would dismiss as just another sexy pinup or whatever, but I do imagine what a fully functional society of animal people might be like, and think they look cool in their own right. Sometimes, you just like what you like, you know? You don't need to have a reason why.
Sounds like yours is a healthy obsession.
Anyway, it's fun to think about this stuff. I'll stop now before I go completely off the deep end.
*listens to the owls in the backyard instead*