I wouldn't publish details of living relatives because they may not want even other relatives to know that they are 10 years older than they claim and got married the week before the birth of their first child.
However, maybe I am naive, but I can't think of any information we usually put into a family tree that could be used for fraud. If anyone wants to steal an identity they have their pick of every entry in the GRO, and getting a birth certificate will give the mother's maiden name. My bank has never asked me for my grandmother's eldest brother's name or my great-grandfather's occupation.
I know that it sometimes seems that we can't trust anyone any more, but given that I am fascinated by the enormous web of connections that went into producing me, and eager to hear from anyone else who is part of my particular web, I am really grateful that we have so much information available, through the government and many private sources, and I really hope that people won't be put off from communicating as freely as is decently possible.
