Brian, with all the niceties intended, I am afraid to tell you you have deeply misunderstood socialism.
A central bank is not key to socialism or communism, ever. Socialism is defined properly as any organized society where allocation of resources is the responsibility of an organized group of people. And in its more elaborate and specific form, socialism is a propertyless, classless, stateless society, with main focus on industrial production, industrial goods, and power of industrial workers.
A central bank is always a private bank. The Federal Reserve is a private bank. The European Central Bank is a private bank. Bank of Canada and Australia are private banks. A central bank is always formed under a government charter given to a private bank to manage its treasuries. Thus, it fails the first criteria of socialism of a propertyless society, because a central bank is private property and formed under division of labour. Even democratic institutions can not interfere with a central bank, and the government is at the mercy of the central bank for its money and funding. Secondly, a central bank is always formed under a state-approved charter, and thus can not be compatible with a stateless society. Thirdly, a central bank may exist in agricultural nations like India or service sector nations like Luxembourg, while socialist societies are always industrial societies; hence it is not key to socialism. Fourthly, a central bank is run by capital and is in the business of allocating capital, and thus is a capitalist institution that still can not be socialist. Fifthly, a central bank can merely make limited attempts to alter interest rates and aim at price stability, but it is not involved in an organized attempt to allocate resources with the involvement of all industrial workers of society, and thus still can not be socialist.
State socialism is a contradiction in terms.
As it is, central banks have existed before socialist philosophy was common in universities, going back to medieval days.
Communists call everything they don’t like as “Liberal”, Conservatives call anything they don’t like as “Liberal”, and today’s libertarians call everything they don’t like as “Socialist”. In the end, it is all the same stupid lie. Differences in people’s views are more important than similarities.