I kinda hit a situation like this a short while ago. I realised that I was actually a furry fan a few years ago, and have kinda embraced it to an extent online. Like, I'm not actively rubbing it into people's faces, but I do express this from time to time with some writing and art that I've been trying to do more of as of late. This has all been online though, afterall, I'm going round with the name StolenMadWolf and a wolf avatar, that makes things pretty obvious.
In real life, I don't really say anything about it. Partly in fear of being seen as weird and screwing up my own opportunities in the process. That included family.
Very recently, after a big row, I ended up having a bit of a freak out and came out as furry to some of my family, whilst also explaining what it was. It actually turned out pretty well in the end, one of them actually found the whole thing quite funny and nicknamed me furball for a while. Now they've kinda forgot about it since then. It helped that I was actually showing them furry drawings of mine, and one of them made the connection that one I was drawing alot of was my fursona.
But there were alot of ways that could have gone wrong. My stance on the matter is this. Is it really that important to mention to someone given it's a hobby? If not, then there is no need to worry. If it is, can you know for sure how someone will actually react to it?
I'm not going to be screaming that I'm a furry everywhere I go, it's just a hobby. Now, if someone makes the connection, then depending on the circumstances, sure, I'll talk about it. But I'm not going go crazy with it.
Maybe drop a few subtle hints here and there without saying anything to test the waters, and gauge from that.