Like the Dreyfus affair at the century and the Sacco-Vanzetti trial in 1921, the Hiss case became the political cause of an era, the more so because it was the first time a congressional hearing was shown on television.
Option Elimination -
To clear some air.
"the more so" and "all the more so" in the majority of the cases act as an intensifier and don't need "than."
E.g., The team's victory was impressive, and the more so because they were playing against a strong opponent. Here, the "the more so" acts as an amplifier for how the victory was impressive. The "so" part refers to the previous clause, "victory was impressive," and further reinforces or amplifies it.
Or The company's decision to invest in renewable energy is commendable, all the more so because it aligns with their commitment to sustainability and profitability."
Here, "all the more so" amplifies "the commendability of the decision." And "because" answers "the reason" or "why" is even more commendable.
The difference between "the more so" and "all the more so" is in terms of the intensity of implication.
"more so" usage is a bit more complicated - It may (require "than" in case of comparisons) or may not require "than" if the comparison is understood.
E.g. John is a talented musician, and Mary is even more so than him. We are intensifying and comparing the talents of two people.
Or The company's profits have increased significantly, and expenses have risen even more so in the past quarter."
In this example, the phrase "even more so" implies a comparison between the increase in profits and the increase in expenses, even though the word "than" is not explicitly used.
(A) the more so because it was - "the more so" further amplifies the previous statement, "the case became the political cause of the era," and "because" shares the reason for further amplification, i.e., why the "the case became the political cause of the era" is further strengthened or amplified. ok
(B) more for its being - First, "the more so" is gone, and we have more. And with just "more" as a comparison marker, we need "than." Even with "than" here, it'll be wrong as there is no comparison. Secondly, "for" introduces the purpose. I bought the laptop for work. There are other uses of "for" as well, such as "preposition of time." For, She studies for three hours, or "preposition of currency," E.g., I exchanged my dollars for euros or "as a coordinating conjunction - FANBOYS."
Saying that the "purpose" of the application was "it's being the first time a congressional hearing was shown on television" does make sense as "the first time a congressional hearing was shown on television" is reason and not the "purpose." The case was not made the political cause of an era to show it on the screen. This is ridiculous.
(C) more for the reason that it was - Again, with "the more so" intensifier gone, we have a comparative "more" which requires "than." Again, the same issue of "for." "the reason" is not the purpose. This is a mess. Let me explain the mess if it's still not clear. "the reason that it was the first time a congressional hearing was shown on television" is the purpose of "the Hiss case became the political cause of an era." or put "the reason is the purpose the Hiss case became the political cause of the era." Moreover, we don't have any comparison here, so even with "that," it'll be wrong. We need an intensifier here and the reason for amplification.
(D) the more so for the reason because it was - Sorry, but it's even a bigger mess. We have "the more so" as an intensifier. We have "for" to introduce the purpose. Then we have "the reason" repeating the same issue as in C, then further enhancing the mess by adding redundant "because" as it means the same as "the reason."
(E) the reason of it being more so is that it was - first "it" referring to the previous clause as in why "the Hiss case became the political cause of an era"? "it" pronoun can't refer to a verb or a clause. "the reason" for what?