Well, it is pretty normal to be shy about something, Myself im not so shy with wearing a tail, ears or a collar around my parents... Though i am very shy with pretty much anything that can relate to furry (exept for wearing a collar which i do almost 24/7 and having my tongue a "little" more visable than usual...) when pretty much anyone can hear or see me...
I won't even wear my collar as a bracelet around them, even though I do it around town and at school and everywhere else.
Usually, people are more shy to do stuff that is not so "normal" around their parents, a close relative or a really close freinds than around other people...
Well, i'd say that the best you can do is either contintue to not wear it around your parents or just put it on and hope they'll have a good reaction to it...