My quick explanation
Though generally regarded as a fairly undramatic, even bland chief executive, many of President Eisenhower's assertions, such as his warning about a military-industrial complex, might have aroused controversy and ire if he had not projected such a genial, middle-of-the-road persona.
(A) many of President Eisenhower’s assertions, such as his warning about a military-industrial complex, might have aroused controversy and ire
his is referring to President Eisenhower’s - possessive case is not a good antecedent
(B) many of President Eisenhower’s assertions, such as when he warned about a military-industrial complex, might have aroused controversy and ire
he is referring to President Eisenhower’s - possessive case is not a good antecedent
(C) it might have aroused controversy and ire, such as his warning about a military-industrial complex, when President Eisenhower made assertions
it - no antecedent
(D) President Eisenhower made many assertions, such as his warning about a military-industrial complex, that might have aroused controversy and ire
his is correctly referring to President Eisenhower - not in possessive case
(E) President Eisenhower made many assertions, such as his warning about a military-industrial complex, that might have aroused controversy and ire even
even sounds odd when compared with D