Totally agree that much of what we do, what we think, what we believe, both consciously and unconsciously is a product of culture and society -- not just the individual.
BUUUUT -- culture and society are created by brains and experienced by brains. So, I expect that you have in your body physical artifacts that map to your understanding of culture, and your history of experiences in society. Like a lossy shard of the whole.
So to say that we can't understand all of this in terms of neuro, or even chemistry, or even physics is wrong and a false dichotomy.
To say instead that psy- studies provide a different (higher) layer of abstraction that is more expressive for describing and understanding certain behaviours is correct.
If you're teaching someone tennis, you tell them where to put the racquet. You don't enumerate the positions of the atoms in the racquet. In the same way, neuro descriptions should be true. In fact more true than psy descriptions, but psy descriptions should be more useful for understanding large-scale behaviour. Invariably they will be a leaky abstraction and we will often have to go down to the neuro level of detail for greater insight.
The other issue is that I think there's a stigma to psy-sciences because of poor replication, and poor statistical techniques. Neuro is supposedly harder science. You can fool the people, but not the molecules. Whether this is actually true is open to debate, but the the psy-sciences definitely need to up their game.