Learn Turkish: Eskiden kimin haklı olduğu aşikâr olmazdı. - In the past, who was right wouldn't be obvious.

Because the entire clause kimin haklı olduğu ("who was right") acts as the subject of the main sentence. In Turkish, sentence subjects take the nominative case (zero case), which means they have no extra case endings added after the possessive suffix.

Why does kim take the genitive ending to become kimin?

In factive noun clauses built with -dIk, the subject of that specific sub-clause usually takes the genitive case. Here, the sub-clause is "who was right". To link "who" with the verb "to be", we use the standard genitive-possessive structure: kimin ... olduğu (literally, "whose being...").

Why do we need the word olduğu here at all?

Haklı is an adjective meaning "right" or "justified". To turn a statement like "who is right" into a noun clause that can be the subject of a sentence, we need a verb to attach the -dIk suffix to. We use olmak (to be) as a helper verb, creating olduğu ("their being").

Why does the sentence end with olmazdı instead of just olmadı?

Olmazdı combines the negative aorist tense (-maz) with the past tense copula (-dı). This combination translates to "would not be" or "used to not be," which perfectly matches the habitual past meaning set up by eskiden (in the past). Olmadı is simple past and would mean it simply wasn't obvious on one specific occasion.