Here is some information about subjunctive's and this question primarily tests one's understanding in regards to the usage of subjunctive
Following words follow subjunctive construction(also list is not exhaustive): Dictate, demand, insist, mandatory, Suggest, Stipulate, recommend, request, purpose
Following words use "to" (also list is not exhaustive): Advice, persuade, forbid, want, allowed
Following words can use subjunctive or to (also list is not exhaustive): Require, urge, beg, ask, desire, Intend, prefer, order.
Here is a possible sentence for subjunctive construction:
The company(sub of the sentence) demanded(subjunctive trigger word) that John(subjective subject) go(plural verb) to the market. Also whenever the subjective words are used we will use a plural verb in the sentence such as in the example sentence above we will say go not goes even though the subject john is singular. The verb of be is always be. Also, do not use should in a subjunctive sentence.
Here is a possible sentence for to verbs:
Lory's friends persuaded her to invite her boss to the party.
So, in conclusion, keep an eye out for these words when you read an SC question. As soon as you see one of these words go through the rules(primarily SV agreement because its contrary to the normal SV agreement). Now coming to this question: In a 1917 meeting of the Shamrock Animal Liberation Front, Joseph Thomson Hardy,
as he was a longtime advocate of animal rights, antagonized many of his most fervent supporters in his demand that giving away pet dogs should be deemed animal abuse.
A.as he was a longtime advocate of animal rights, antagonized many of his most fervent supporters in his demand that giving away pet dogs should be
(Wrong: Whenever there is a subjunctive word we can not use should with it in the same sentence) B.as he was a longtime advocate for animal rights, antagonized many of his most fervent supporters by his demand of giving away pet dogs being
(Wrong: In subjunctive structure the verb of be is always be not being)C.in being a longtime advocate for animal rights, had antagonized many of his most fervent supporters with the demand that giving away pet dogs should be
(Wrong: Same error as option A we cannot use should and the word demand together) D.a longtime advocate of animal rights antagonized many of his most fervent supporters by demanding that giving away pet dogs be -
(Correct Verb of be is be and we are not using the word should with a subjunctive word demand) E.a longtime advocate of animal rights, he antagonized many of hiscannotervent supporters in demanding that giving away pet dogs should be
( Wrong same errror as A can not use should) Hope it helps. Also
SugandhaM you might enjoy this question.