My parents kinda had that too. When I told them I wanted to go to a furry convention, they didn't know what to expect. I already explained them trice what furries were, they kept forgetting so I didn't bother to explain that part. Instead I just gave them the ability to look at the website of the con. They were worried in the beginning, since this was the first time I went on vacation alone and being with a whole bunch of people nobody in this house knew. Also they expected that I disliked being at the con...?
Anyways, for me it worked out just fine. It might or might not work in the same way for you. For me saying I'm going to a furcon just as casual as I'd say I want to go to a zoo would've worked. Except I'd do it with more exitement.