I could be wrong but I don't think he's a dualist. He rejects human consciousness being computable on classical computers, like Turing machines, but thinks that quantum stuff is necessary. Quantum brains/computers are or would be computing in our physical universe, making him a materialist not a dualist. His big thing is using this quantum stuff to free his own mind from the confines of Gödel's theorems (I think for egotistical reasons.)

Simultaneously, actual dualists flock to his theories because they think association with Penrose lends credibility to their religious stuff.