Non-personalized Prepaid Mastercards

I've been reading with great interest the two threads on BOL regarding the [Name of tax preparation service withheld] Prepaid Mastercards. We've had many questions already from customers and non-customers about getting cash advances from our branches with these cards. I am concerned particularly with the non-personalized cards (i.e., no owner name on the card) that are issued by [Name of tax preparation service withheld]. According to our information, these non-personalized cards are issued "on the spot" to the [Name of tax preparation service withheld] clients, with very little explanation. (They are given disclosures.) If a client wants to get a personalized card with their name, it takes several other steps and several more days to get the card. We believe we're mostly going to be seeing these non-personalized cards. Do we have the right to refuse to handle the non-personalized cards, especially for non-customers, or because the card is a Mastercard product are we required to accept them?