Stablecoin Classification and Regulation Act of 2020 This bill provides for the regulation of stablecoins, a type of privately issued digital currency whose value is pegged to a currency such as the U.S. dollar. Issuers of stablecoins must be a member of the Federal Reserve System, and must seek prior approval from the Federal Reserve, the Federal Deposit Insurance Corporation, and the appropriate banking agency for the offering of stablecoins. Issuers of stablecoins are subject to oversight by the appropriate banking agency, including with respect to capital adequacy, leverage, and permitted activities. Furthermore, issuers of stablecoins must be able to redeem all outstanding stablecoins at their nominal redemption value in U.S. dollars upon demand.