If I want to tell someone, I usually get VERY nervous and it won't come out, it feels like words go back to my stomach and make a spring cleaning there (the type someone else is obsessively doing, and when you try to go anywhere, you get stuck between loads of moved furniture, with piles of dirt everywhere), and the feeling won't go away until I completely dismiss the idea, and move pass any subject related...
If however, I casually mention it like just anything, I get it out easily, like:
You: Wow, you sure have a lot a plushes, don't you?
Me: Of course! you would expect from a Furry.
or
You: Is your Nintendo 3DS charged? can I play a bit?
Me: Sure!
You: You know... Nintendo DS is called "the Video Game of Pokemon", isn't that strange to a grown men like you?
Me: No stranger than being a Furry!
So I guess my trick if to not make a big deal out of it, it's just like saying, i write songs, I can fix your PC, or I like Kingdom Hearts and Steven Universe, is just a part of me, that I don't need to overthink,
that's what works for me anyways, otherwise I drop some obvious clues, but that's another thing.