Well, I don't believe that a social movement has to have a formal organization behind it and this is proven by Bitcoin right now. Or we can say that Bitcoin is a decentralized social movement...that can be the right term. Now, if the idea is to have an organization behind it because it is a social movement, that will be against the very idea of Bitcoin itself so in other words it would be a contradiction in itself. Bitcoin succeeded because of the people who believe on it and this will be the same throughout its existence.
Yes, it is true, social movements do not have to have a formal organization. And speaking of contradictions with the Bitcoin idea, I don't think it is. If Bitcoin has to form a formal organization, it can too. Bitcoin economically has provided many benefits to its users and financial freedom was felt by those who held holdings in the past. This means that Bitcoin is trusted by many people and also provides many benefits for everyone.