Although once they had sought equality by appealing peacefully, the So

first of all, we are comparing a past situation with a present situation, the correct way to compare that is although. Then, the first part of the underlined portion says that they did something, and the second portion refers to the way they did the thing. So correct preposition should be by.
Now lets take a look to each of the alternatives

a. Although once they had sought equality by appealing peacefully
they used although and by, so lets keep it

b. Where once they were seeking equality by appealing peacefully
where is used to indicate a physical place, so eliminate

c. When once they sought equality by means of peaceful appealing
when is used to indicate an specific time lapse, but here is a comparison between to different times that are not specified.

d. Although once they had sought equality in appealing peacefully
right usage of although but not sure about the preposition "in". keep it for now

e. While once they sought equality by appealing peacefully
while is used to indicate 2 things that occur simultaneously, and here are 2 situation that are sequential

Now we have D and A, but as I said before, the second part of the underlined portion is saying in which way something were made, so correct preposition should be "By". Also By is parallel with the non-underlined portion.

X did something by, X were transformed by

IMO A