I think I have read the claim that he was both an idealist and a materialist and not a dualist, but what is mind independent for him, trees, colours, electrons?
I interpret "realist about X" as meaning "thought of X as real".
But then, your OP speaks of "mind-independence" as a criteria for what is "real". Merleau-Ponty considered that any knowledge we have of the world is derived from our mental representation of the world, that the whole world as we see it is by definition mind-dependent, and that philosophy is about our presence in the world. It's not about trying to figure out "how does the world look like when no one is looking."
So I would say that your criteria of mind-independence does not really work for Merleau-Ponty. It is not his concern.