Being a Furry only means your interested in anthropomorphic animals. Simple as that.
They barely have any reasons to not accept you, Just explain it to them truthfully and tell them about the false stereotypes (Gay, f**k in costumes and all that crap), It barely means you're gonna change, Many people like anthro animals, Like Sonic, Crash, The list goes on.
Let them see the good side of the fandom and not the stereotype media has created, I'm sure they'll accept.