I say that there is nothing deficient about our current theoretical grasp of mind-brain identities. The problem is only that they are counter-intuitive.
Philosophers sometimes also use 'reductionist' more strictly, to mean 'type-identities' between mental and physical categories, and to exclude 'non-reductive physicalisms' like metaphysical functionalism.
I'm not so sure that I am a reductionist in the strict type-identity sense. The issues here are messy. But I certainly a reductionist in the more general sense which is opposed to eliminativism and dualism.