Principal concerns with genealogy data are how it can affect identity theft. Some feel that genealogy databases are a rich seam for fraudsters. Others feel that these concerns are peripheral. In my case, my personal details have been recorded in publically available material since I was born. So my date of birth and mother's maiden name are easily accessible. Does this make my identity easy to steal? Well, may be not. Using my date of birth or mother's maiden name as a password or proof of identity would not be my first choice. Or if it had to be used, then should only be used as one part of the security process.
Some websites have a policy of not publishing details of the living, so even if you have a family link to Queen Elizabeth, or President Obama, you cannot show them!
Several of the genealogy websites do have good discussions on identity theft, and they are worth a read. However, I offer caution in going overboard in supressing information that is already public, as some seem to suggest.
Try Family Tree Magazine
for further reading.