If you commit a crime, get caught, and that makes people trust you less in the future, that's just the natural consequences of your own actions.

No, I don't think if you shoplift as a teenager and get caught, charged, and convicted that automatically makes you a shoplifter for the rest of your life, but you also don't just get to wave a magic wand and make everyone forget you did what you did. You need to demonstrate you've changed and rebuild trust through your actions, and it's up to each individual person to decide whether they're convinced your trustworthy, not some government official with a delete button.