In my view, the right answer is option C.
Option A: Known as the Australian Eleanor Roosevelt, Jessie Street lived a life
in privilege while at the same time
devoting her efforts to working for the rights of the disenfranchised, including workers, women, refugees, and Aborigines.
The use of preposition
in is inappropriate in option A. The right preposition should be
of. We can, therefore, eliminate A.
Option B: Known as the Australian Eleanor Roosevelt, Jessie Street lived a life
of privilege
while simultaneously she devoted her efforts to working for the rights of the disenfranchised, including workers, women, refugees, and Aborigines. This option is not concise. There is no point in introducing the word simultaneously after while.
Option C: Known as the Australian Eleanor Roosevelt, Jessie Street lived a life of privilege while devoting her efforts to working for the rights of the disenfranchised, including workers, women, refugees, and Aborigines.
This is correct and concise.
Option D: Known as the Australian Eleanor Roosevelt, Jessie Street
lived a life
in privilege and
devoting at the same time her efforts to working for the rights of the disenfranchised, including workers, women, refugees, and Aborigines. the preposition in is not appropriate. and devoting suggests parallelism. A scan through the sentence reveals there is no element that can be made parallel devoting, apart from the verb lived, and this is not right. Eliminate option D.
Option E: Known as the Australian Eleanor Roosevelt, Jessie Street lived a lived a life of privilege and wealth while [i]
at the same time[/i] devoted her efforts to working for the rights of the disenfranchised, including workers, women, refugees, and Aborigines. This wordy, there is no need to introduce the phrase at the same time.