Without knowing the nature of the charges, the age of them and whether there are convictions, I can't say if I would or not. I'm not going to dismiss someone out of hand simply because they have made mistakes, especially if their credit is good and they have good prior LL references.

I'm not sure there is a way for you out of it if you're already told them they've been accepted. If you say something came up in their background, they are going to ask what. Depending on how you handle it, that could blow up in your face and you get sued. If you don't offer them a reason, they will have no idea and may jump to it being about race. Then it blows up in your face and you get sued.

The way I see it, you are stuck. You should go ahead and let them stay, they may be the best tenants you ever have. They may not. Don't go hunting for reasons to evict either. Because unless you watch every single tenant with the same level of intensity as them, they may assume it's because of race. Then it blows up in your face and you get sued.