Cashing a check does not trigger CIP requirements; your CIP requirements do not apply to check cashing unless you have explicity indicated that they do.
Although it does not make any sense to me, banks are oftentimes more liberal in their ID requirements for cashing checks than they are for account opening; i.e. if you want to accept ID from a fantasy organization to cash a check when you would not accept it for opening an account, you may do so.
OFAC checks on payees are a function of policy, not a legal requirement. However, if you accept fantasy ID, you geld your OFAC check in violation of your own policy. So, back to square one.
Your bank should (not must) have written identification standards for check cashing. Your concern is not with the payee's beliefs, you have no contract with the payee. Your concern is with your customer; i.e. the person who wrote the check. I suggest you contact the customer who is issuing checks to this person and say that from now on your ID requirements are...
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.