I don't think money is entirely political. It started off as a technical solution - an abstraction of value from things themselves to things (coins) that represent value, all based on an understanding that everyone would agree that the coins represented a certain amount of value. Of course this is simplifying it, because coins were made of silver etc that already had an agreed value, but I think the basic point holds.
Banks are under the Government, the government is the one who make the call on what to do about the fiat that is being printed when it is needed. For me money is entirely political because they are the ones who is controlling it, they are using the banks to make it compact and well organized while citizens are using it on their everyday lives that keeps the economy moving, just my opinion, you don't have to believe it.
Its more then your opinion, banks need to follow the rules, rules set by government. Every country is different, in some countries banks have more power, in others less, point is that they have a deal with government. For example interest rates are different everywhere, in some countries citizens are protected until some level, in others banks can have power to do what they like, of course with the deal with government.
Money is political, and banks are politicized. In my country the Governor of the National Bank is a politician. That speaks for itself.