The local Post Office in Quincy accepts the Gene Grawe Fund’s Five Back Visa card when paying for postage and supplies. So does USPS.com.
I would imagine the outlying Post Offices can also.
Today, I used a registered Five Back Visa to purchase some stamps online and it went fine. I can’t say what would happen if you tried to use an unregistered card. During checkout, I noticed that you can also pay via PayPal. Which means you can also pay using a GGF Visa through PayPal.