Your family is part of your private life more or less by definitionYour family is part of one of your private lives. Having others can be healthy. Depending on your relationship with your family, very healthy.
And, yes, you still have to make sure that your stuff posted online passes the New York Times test: If it turns up as front page news you have to be able to survive. That said: The advantage of a social network with loudly stated privacy norms is that (a) people will be told not to share outside the list, (b) you can control which friends are on the list and hopefully keep the untrustworthy ones out; (c) when people cut-and-paste anyway, despite your precautions, they can be properly ostracized, which (one might hope) will teach them some manners.
