In evaluating the challenges faced by female politicians, the question of whether their qualifications are as respected as those of their male counterparts is paramount.
It is unclear what is the main clause of the fully underlined sentence with modifiers. So let's breakdown the sentence in parts and keep the meaning closer to the original sentence and not deviate.
1. There is an evaluation of the challenges faced by female politicians.
2. There is an important(paramount) question in that evaluation.
3. That question => Whether the qualifications of female politicians are respected as = those(qualifications) of their male counterparts
=> In the evaluation, the paramount question is whether the qualifications of female politicians are respected.
Look for, for as...as comparison in the answer choices and there seems no comparison errors. Rule out comparison issues.
So, the problem is the ordering of the modifiers in the sentence.
Notice several of the answer choices uses the 'they' pronoun and it must refer to the female politicians.
(A) In evaluating the challenges faced by female politicians, the question of whether their qualifications are as respected as those of their male counterparts is paramount.
The phrase 'In evaluating' is actually modifying, 'the question'. It seems that the question is evaluating the challenges faced by female politicians. It should, actually, mean: 'In the evaluation of X, the question of Y is paramount'. i.e., inside the evaluation there is an important question. So Eliminate.
(B) The question of whether the female politician’s qualifications are as respected as those of their male counterparts is paramount in evaluating the challenges that they face.
Female politician's means singular. 'They' usage causes pronoun reference error. Eliminate
(C) A question that is paramount in evaluating the challenges that female politicians face is if their qualifications are as respected as those of their male counterparts.
Notice, whether is more suitable than incomplete 'if condition' usage. Also, the intended meaning is changed. 'The important question is evaluating the challenge' differs from the original meaning of the sentence, due to misplacement of the modifiers. Eliminate
(D) The question of whether the female politician’s qualifications are as respected as those of their male counterparts is paramount in an evaluation of the challenges that they face.
Same issue as in option B. Eliminate
(E) In an evaluation of the challenges faced by female politicians, the question of whether their qualifications are as respected as those of their male counterparts is paramount.
So the best answer choice is E.