What you do is decide what you care about from a conviction perspective (say, crimes of dishonesty, serious violence etc). Then you write up a policy that says these are exclusionary. Then you only let HR run background checks immediately pre-contract, and you don't let anyone outside of the immediate background check team see any of that stuff. They're empowered to give you a yes/no to hire, but that is all.

Hiring managers should not be looking at BGC material.