In the feminist movement of the 1960s, women began to join the workforce in large numbers, in despite of the fact that many had worked during World War II due to the decreased male workforce.
If i rearrange the original sentence, then it may look like
In despite of the fact that many had worked during World War II due to the decreased male workforce, women began to join the workforce in large numbers in the feminist movement of the 1960s.
In despite is incorrect usage despite alone is correct. So, A is wrong.
A. in despite of the fact that many had worked during World War II
E. in spite of the fact previously that they worked during World War II - Seems better option but placement of 'previously' is incorrect here. To whom it modifies??? Still hold it. It might be better if previously placed before worked.
B. whereas previously many women had worked during World War II - there is no contrast word (as original sentence) here, otherwise there is no error. Still hold it.
C. whereas previously there were many who worked during World War II - previously is incorrectly place. many refers to what? Incorrect.
D. whereas previously those many women who worked during World War II - Modifier error, those??? Incorrect.
Out of B and E, i think B is better than E though not the best one as it does not contain the contrast meaning and E seems wordy & placement of previously.
Women began to join the workforce in large numbers in the feminist movement of the 1960s, whereas previously many women had worked during World War II due to the decreased male workforce.
Imo. B