I've gone through tons of background checks / drug screens for federal and state governments, and financial companies. But I've never had a Facebook search...
Is that even legal?
"I'm sorry, I don't use Facebook as it seems an invasion of personal privacy"
or
"Ok, here's my Facebook account" and then give them some uber-sanitized account that just has photos of kittens and messages on your mom's wall about her cookies.
It works best if you're actually in California, but even if not, it might give them pause.
Later, I worked on some of their creepy background checking software. Essentially, without the login, they can still get all the information about me they need.
4. You will not share your password (or in the case of developers, your secret key), let anyone else access your account, or do anything else that might jeopardize the security of your account.
It's not iron-clad, but it may dissuade the nosy.
I have to check my Facebook every few months to find out what sort of content is now visible to a new group of people that was hidden by me in the past.