As someone who DID tell my parents I was a furry when I was probably about the age you are now, I have some thoughts.
1: Take a good look at your situation. Do your parents accept alternative lifestyles? What do they think of people who dress in alt fashion? Do they particularly care about cosplayers? If any of these answers are negative, I don’t think you should bother telling them.
2:Being a furry is not something where you need to “come out”. It’s perfectly okay to enjoy the furry fandom out in the open and never have the conversation of “hey, I’m a furry”, because in my experience, parents don’t care. They don’t. Truly. Unless you’re in a situation where you think it would be BENEFICIAL to tell them, just don’t.
My parents are well aware I’m a furry, hell, I’m actively making a fursuit on the kitchen table. And while they think it’s weird, and they don’t want me attending conventions until I move out, they aren’t any different. Most parents are just like this. So truly, if you don’t feel like you need to tell them, why bother?