certainly don't tell the other half.
As to the offending half... well, I once found a colleague sending highly libellous emails via the office system unaware they could be read by anyone who knew about the folder that contained copies of absolutely everything. I told him of its existence, without specifically mentioning his emails, and he went rather pale... but boy, was he grateful.
If you think your family member doesn't know their posts can be seen by others, and should know, perhaps you could try the same thing. Don't sound judgemental or mention your worries, just say "did you know..."
Then never mention it again.