No passport

Mexican non-customer requests to cash a check between 5- 10,000 for labor.
He states he does not have a drivers license (even though he did drive to the branch) or a passport. Only has a Mexican voters registration card.

Do banks need to police whether a person does or does not have a passport and file a SAR?

No - but you don't have to cash the check either.

The person that wrote the check will have to withdraw cash to pay him.