Being in a profession where I am required to have annual background checks, I don't have an issue with it, because I have nothing to hide. Maybe if I had something embarrassing on there, I would think differently. I also think the safety of children trumps our desire for privacy.
I have received background check results from people applying to be foster or adoptive parents that had disqualifying offenses on them, including violent crimes. Even knowing that they had committed violent crimes, they tried to work with children. People make choices, and choices have consequences. I wouldn't want a person convicted of a violent crime or abuse of a child to hold any position that has anything to do with kids. To me, there couldn't be a bigger red flag.