In Ukraine, Fidobank offers "Shtuka" (Штука, translated as "piece" or in jargon "thousand") debit cards that are attached to MoneXY account that is in turn attached to mobile number only. And since prepaid cellular service is mostly anonymous here, you can actually have as many anonymous accounts as you can for about 60 UAH (a bit more than 2 USD) each. And still these are physical MasterCards you can put into your pocket, accepted at any supermarket and also suitable for online transactions.