Today I though about telling my mom I'm gay (or bi) and furry.
Me and my mom are very close, there is nothing that can cut this bond (except for the obvious 5 letter word). 2 years ago (I was 12 years old) I told my mom I watched porn (straight that time), I must admit that her reaction was quite good. We talked about it for a night (we started talking while having dinner at McDonald's), she told me her experiences and such. At the end we all laughed and she didn't block me from anything and she understood very well.
If I told her I was gay (or bi) and furry I can't imagine her going past the "Are you sure?" mark, she would accept without any worries.
The rest of the family... weeeeellll that wouldn't be so easy. My father died in 2002 and I didn't get to know him enough to say if he would accept it or not, my two brothers though. Those certainly wouldn't know until I'm like 25