I just posted this in another thread...but unfortunately as long as the facility isn't discriminating against a protected class, they can decide who they want to hire or not hire, for whatever reasons they want.
It's not always fair, I agree. I also agree that you should not be punished forever for a mistake made several years ago, especially if you've turned yourself around. However that's up to the facility
If you don't go to the interview, there's no chance whatsoever of you getting the job. If you go, there's a chance...it may be small but there's a chance. So I would go and show them how much you've learned from your past mistakes.
Best of luck in the hunt!