If you consider money to be a form of speech (I don't but it's been successfully argued in US case law) then I'd argue it is a right as I'd argue availability of anonymity is a prerequisite of free speech.
Whenever one makes a purchase, the price structure of the good that was purchased changes, and in the case of goods/assets that have a yield, it also changes its interest rate structure. This is information being propagated from the consumer to the merchant, via the price system, using money. So while the act of exchanging money for goods is not information in and of itself, as speech is, this act results in the propagation of relevant information from consumers to merchants to producers.
