I would be fine with credit checks and criminal background checks being run on all final stage candidates, with consent. I hired a felon once and ended up losing seven figures. Not doing background checks on someone in a key position with access to customer information, etc. seems irresponsible.

A low credit score should not be a disqualifier, but should be explained. If someone had gotten divorced or medical expenses or something, that isn't a concern (and I would consider advancing money to clear it up for any clearance investigations later), but if it is due to gambling, drug, etc. addiction, I would be very dubious unless there were a way to show it was not an ongoing risk. (similarly, there are some criminal convictions I would consider benign or even slightly positive, and others which would be disqualifies)