Is there a risk that these service providers will follow CRS and report account balances back to our tax agencies? I am looking for a EUR card that I can use for normal living expenses. I would prefer not to be charged with tax evasion

All banks share information.
http://www.oecd.org/tax/transparency/automatic-exchange-of-informationSeriously, better keep away of non-cash fiat of you want to avoid such a thing... Bitcoin is a good alternative I would say...

But not all banks are connected. Within some countries yes, but on the general level no and something like this is impossibe to establish.
Also they don't exchange information without reason and automaticly so I think such fear have no ground
But I agree that Bitcoin is solution, although not perfect, if you want to completely avoid personal data exposure. But even with Bitcoin your data and transactions are not completely anonimous, don't forget that.