In USA, the privacy issues are likely tied to the state law on background checks. (Outside USA, I don’t know the laws as well, but privacy laws are usually even more stringent outside USA.)
Normally, an employer cannot share information it finds during a background check with people or entities outside the organization. It can only use that information for the purpose of doing its own background check. I would guess the same thing likely applies for volunteers or any other person whom the organization performs a background check on.
In USA, we have the public registered sex offender lists as a form of public notice about sex offenders in one’s neighborhood, in order to protect children, and there’s enough controversy over that without allowing every diocese or employer to tell other dioceses, employers, organizations etc that Joe Smith has a prior conviction.
And I don’t have any problem with parishes and dioceses wanting to protect their money; it’s donated by the parishioners in that diocese, and we would all prefer that it goes for the things we intended it for, such as diocesan administration and building maintenance, rather than into the pockets of somebody bringing a lawsuit. That’s just good stewardship.
If someone is making money off a paid speaking engagement, and has passed a background check in his home diocese, I’m a bit mystified why he’d make a fuss about going through a background check in another diocese, but it’s his choice whether to go through the check for the purposes of making the money, or skip the background check and forego the engagement and the pay for it. I don’t think dioceses should have to adjust all their processes just because some invited speaker refuses to play by their rules.