It's about honesty. Some gay people come out to their parents, so zoos can come out to their parents as well (assuming that one's parents won't "spread the word" to other people). It also depends on the attitude of one's parents, and whether one's parents can be trusted to keep a secret. On Beast Forum, some zoos said that when they told their parents that they were zoo, they learned that their parents were also secretly zoo.
It seems most zoos are very secretive and dishonest (secretive in relation to family members). Note that I'm using the word "dishonest" in a literal sense (in other words, not as a value judgement). There's nothing wrong with hiding zoo interests from one's parents -- each situation is different. That being said, there was a poll like this on Beast Forum, and about 80% on the BF poll didn't tell their parents -- but the poll on this thread is 97% of people not telling their parents.