You haven't given an objective reason for preferring objectivity. So I guess it's a personal preference you have that others don't share.

Discussing personal preferences makes not much sense. They can coexist and both be valid. One person likes blue and the other red. But in terms of objectiveness, there is only one truth that can be reached.

It is an objective fact that one person likes blue and the other red, this is not meaningless, though of course it's unfortunate to forget about a person-reference [LW · GW] in such judgements. Person-1 likes blue, person-2 likes red, the "likes" takes two arguments. Both judgements coexist and express personal preference, it makes sense to discuss them. It's an error to confuse person-references and equivocate between the judgement that person-1 likes blue and the judgement that person-2 likes blue, as these are different judgements, truth of one of them doesn't in general imply truth of the other, though it might serve as weak evidence.

If a contradiction happens in the story then this is an undisputable flaw.

Why? Maybe the story has an unreliable narrator, and an alert reader should pick up on the contradiction in order to figure out that the narrator is unreliable. Maybe the story is being told from different points of view, and different parties are offering differing interpretations of the same events. Maybe the story is a mythological one, descended from oral traditions, and contradictions have seeped in from the fact that many different people at many different times have told the same story, each adding their own flavor.

There's lots of ways to make contradictions work in a story.