well being furry means being a fan of anthromorphic characters
and if your parents like cartoons that have those types of characters
BAMO they are a furry subconsciously
rememba, appeal to intrests, test the water (by asking something different, ie. their stance on something, if they answer biasedly, ask them if they actually believe that, if yes then just dont tell them, if not theres a risk involved but im not sure)
be the diplomat