How can I keep myself from saying anything that might give too much away?

Ok, I have been a furry for quite awhile. I haven't told my parents, as they'd literally judge me to death. I really want to get more active in the furry community, and ive already had a furhead commissioned for me, but I'm worried that if my parents find out about me being a furry they'll find out about my sexuality as well. If they don't understand furries they'll sit me down and have me explain and I don't want to accidentally say too much. I guess what i'm asking is, How can I hide my furry side from them and if they find out how can I explain it to them without giving away my sexuality? I really don't feel ready to tell them as of yet.
Thank you so much! All advice and help is more than appreciated.