A metaphor »invisible hand« coined by Adam Smith is one of those metaphors that caused more harm to the concept behind than any of possible opponent could.
This metaphor is strong, because it refers to something that every human being can understand. Hand. Hand can be nothing but a tool of an agent. This agent can be either something physical (a part of a concrete body, of a concrete agent in a Gea biotope), or something metaphysical, like God. In both cases and in any case it is clear that we can not attach hand to something, that is not an agent. We can not perceive a hand without a specific force with a specific interest moving it; and that is an agent.
Unfortunately for metaphor and fortunately for Adam Smith what he meant with this metaphor goes directly in the opposite direction than to understand any kind of agent behind the market. The essence of a market lies in the fact, that there is no agent behind. Like there is no agent (homunculus theorem) behind human brains, there is no hidden force impersonated in the hand metaphor. There is no central command of human brains. There is no agent behind human brains. Human brains are a part of a larger network (meme complex) and are reproducing this network, in other words: coevolving meme complex.
Market is an emergent property of a complex system of values being there for the sake of exchange.
This is why it is impossible that a deist could really understand and (or) support free market economy. Either he believes in an invisible hand (of God) and thus contradicts the concept of free market, or he apprehend free market and thus exclude any option of such a God that would have any influence on human life. Because: the essence of human life is an exchange of goods. If this exchange is forced, if values are centrally dictated, then this is not exchange any more, but dictatorship. If God provides the value of any thing, then this is not human value any more. Human values are emergent property of »us« only if they are result of exchange on the free market of values. If we understand that there is no difference between value of meme and the value of any good; if we understand that the value of a good is encapsulated in the value of a brand (meme), than we see, that we live in one market only: free market of a meme (values) exchange. No invisible hand is ruling this market. We are our own enemies (and friends).
Even more interesting reasoning goes in the contrary direction. If an atheist believes in centrally governed market (welfare state) then he is in fact a deist! He in fact pretends to be atheist and lives in cognitive dissonance. You cannot be atheist and at the same time support welfare state.
I would dare to state that exactly fear of »me« being the only responsible agent is the cause that humanity dreams about any kind of invisible hand that would relieve »me« from this responsibility. That is why we do love to talk about humanism (something abstract, there somewhere..) and not homonism, that clearly places individual responsibility.