Bourdieu's solution to overcoming this false dichotomy is really elegant. He first considers the objective structures that constrain an individual's thoughts and representations, a social topology. This is all that structuralists generally consider. However, for Bourdieu this is still not sufficient. Instead, he argues sociology must also "elucidate the perceptual and evaluative schemata that agents invest in everyday life". He then conjectures:
"There exists a correspondence between social structures and mental structures, between the objective division of the social world-particularly into dominant and dominated in the various fields- and the principles of vision and division that agents apply to it"
I think there is an interesting parallel with arguments by scientists about how there must be a correspondence between environment and neural structures. They argue (fairly successfully) that sensory systems- such as vision- are imprinted by the environment they are in. Neural coding is optimized for the environments we see the most. In essence, the environment sets the desired dynamical range for the process under consideration. Using information theoretic arguments, nueroscientists calculate the coding schemes that optimize the average information that the brain can extract in this dynamical range. Actual biological neural schemes are surprisingly close to these optimal schemes.