i think too many people are doing this, the stream's posts are encouraging others to do the same, i thought about doing it too, but i didn't want to because of, well, autism, bullies, i honestly will not, but its YOUR choice.
It's not exactly "coming out" per se, but here's a couple questions for you to think about before telling them:
Do they know what a furry is? And if so, what do they think about them, and what would their reaction be when you tell them?
Coming from a guy who has caring parents, I'll just let you know that a real parent cares for their child no matter what they choose to be as long as it's not anything bad.
Oh lol might wanna try posting in the lgbtq stream for more help, but still the last sentence I mentioned. If your parents truly love you for who you are on the outside ,then they will love you in the inside too.
You never really know how they would feel about it, plus you might have to explain why, and when, and who...
I tried coming out to a friend once and she didn't understand it AT ALL. I had to play it off as a joke so I wouldn't have to get into... Detail