Many psychologists believe that while some poor choices by parents can certainly damage their children's social development,
no family can truly be expected to check or limit all of the complicated social media that shape a child's awareness of the world.
This is a compound-complex sentence. ‘While’ marks the beginning of the subordinate clause and the subordinate clause should be truly be followed by an IC A. no family can truly be expected to check –
The concise correct choice
B. no family can be expected that it really checks – expected that it checks is wordy and unidiomatic.
C. that no family can truly be expected to check --- This part is no IC and hence a fragment
D. that no family can truly be expected that it checks ----This part is no IC and hence a fragment
E. that it cannot be expected that any family really checks -- This part is no IC and hence a fragment