According to me, construction of the word support is the crucial factor in this sentence. Option B, D, and E have awkward constructions: for the support of, in supporting, and in its supporting of respectively.
Therefore, we can shortlist A and C.
Now, closer scrutiny of option C reveals that ‘the prejudices were regarding to the imposition of the align taxes ( acquiesced to the prejudices in support of)’… whereas the sentence suggests that support to the impositions of taxes is the action taken by the union, hence, “acquiesced to the prejudice by supporting taxes” is the correct expression.
Moreover, if we reverse the first part of the sentence, before the comma, then Option C becomes “
In support of imposition of taxes, the union had acquiesced to the prejudices”. This construction becomes awkward. It should be – to support/by supporting the imposition of taxes, the union agreed to the prejudices. We have one of the correct expressions in “A”.
Also, "while" is normally used to show the contrast, which is not there in the sentence. I have no idea about whether, “where” is correct or not but “while” is definitely wrong here.
On the basis all above mentioned information, The answer should be “A”