Think most have already been said, so i'll just toss some of my own coins in here ^^
"coming out" as a furry is not needed as it's only a hobby and subculture.
But if you are hugely invested in it, telling people that you are a furry is often a good idea unless your gut feeling says otherwise..
If you only hold it to yourself, there is a risk that it will grow into feeling that it is something to be ashamed of, and can start to be a burden in relations.
And it does not feel good with constantly creating lies or dodging questions for covering it up.
I'm a pretty open person, and would start to feel awful if i needed to cover large parts of my life up.
But i also don't have the urge telling everyone about it, just the people that is close to me :3
But in the end, it's your life, only you decide how to play with the cards given to you ^^
Recently told all my family, friends and coworkers that i was a furry.
Sent them some pictures of me with fursuiters from the con, with a short review of my experience from it and how fun it had been.
When i came back to work, some coworkes actually bowed to me and said it looked awesome.
It really made their day and now i feel i can be the true werido i am with good confidence
Edit: would never ever have told anyone on my previous workplace, was not close as good of a vibe there.
Most "negative" reaction i got was from a friend, but it was more that he was happy that i found something i liked, but he don't want anything to do with it.
And that i can accept, it's not for everyone ^^
If friends can't accept what you do for fun, then it's a clear sign of a really shallow friendship.