Well actually, there is a little more to it I forgot to mention, but it's kind of obvious
You might already know this, but some people are so socially stunted from bullying, child abuse, and what have you that online friends are the only kind of friendships they can ever make.
Fursonas are basically that gateway to online friendships in the furry community.
It gives other people a first impression of who you are as a person and what your interests are.
You ever play VRChat? It's like that. If you find the character appealing, you're more likely to strike up a conversation with them.