1. How would someone else know that the person did X?
2. What if that crime had nothing had bearing on the position?
3. What about the concept of a sentence representing the 'complete payment to society'? Denying someone the ability to make a living turns a finite sentence into an indefinite sentence.
For me,
1. If someone was guilty of embezzlement, this would be relevant (positive or negative) if the position involving money handling (cashier, or accounting) - but not relevant if the position was social work.
2. If the person was guilty of stalking, a position that would allow access to customers' PII would be problematic.