A bank can refuse to cash a check merely because the customer is rude or improperly dressed and there is nothing that customer can do about it. I have even heard of customers being carted off the property for cursing at bank employees, courtesy of the sherriff.
The FDIC controls overall lending and bank regulatory matters, not things like customer service, or which items are or are not paid. There is no obligation to cash checks.
If a bank said they won't lend money to hispanics or if they were involved in predatory lending or some other threat to the financial foundation... then the FDIC can step in. If the banks falsely advertise their interest rates or whatnot...
The only thing that even comes remotely close is the Expedited Funds Availability Act and that does not in any way concern a check casher.
The Expedited Funds Availability Act requires all banks, savings and loan associations, savings banks, and credit unions to make funds deposited into checking, share draft and NOW accounts available according to specified time schedules and to disclose their funds availability policies to their customers. The law does not require an institution to delay the customer's use of deposited funds but instead limits how long any delay may last. The regulation also establishes rules designed to speed the return of unpaid checks.
Go here for a more complete list of what they govern.