A good story can be told a couple of ways.
Hmm... Yes, but no. A good premise can lead to many stories, each told in an unique way, but they would be different stories.
The fact that the incest relationship is a secret or not is a radical change. Not only NPCs will not react in the same way, but even the protagonists will act totally differently, influenced by those reactions. Take the classical, "come on mom, I take you to a date". If the relationship is, or have to be, a secret, the date will obviously be totally different than if it's something that is known.
In the first case, the mother will not be at ease, scrutinizing the crowd, staying cold, too cold for a mother, by fear that people would uncover the secret. As for the second case, it's in fact the second "cases". It would totally change, depending if incest is accepted (most NPCs will not care), tolerated (globally half NPCs will not care, and the others frowns), or condemned (it will not end well).
What I find boring is when NPCs know about the incest and are uninterested. "you're having sex with you Mom? Big deal, let's fuck."
Why should they be interested ? I don't care what people do in their bed and with who they do it. Whatever if they are homosexual, incestuous, or whatever, as long as it's effectively consensual between people able to fully consent ; so no p*d*philia, abuse of mentally challenged, and things like that. It's they life, it have 0 influence on my life, why should I feel concerned or interested by it ?
And this have nothing to do with acceptation. Feeling uninterested doesn't imply that you approve, just that you know it's not your place to judge. As long as it hurt no one, physically, psychologically or mentally, you just let them live and face the consequences if they happen. At most, my reaction face to an incestuous relationship would be, "hmm, don't you fear for your children, if you want some ?" And it wouldn't be a question of health, but of sanity. They haven't asked to be the offspring of an incestuous couple, yet they would suffer from this each time they'll encounter close minded persons.
I know that I'm perhaps not part of the majority, but I'm also far to be an exception. But all this depend of where you've been raised, because it's mostly a cultural thing.
This being said, the answer to your question totally depend to the story you want to tell. But if such a central part of its background can be changed at will by a poll, then you should think again your story. Unless you're a talented writer in search for a challenge, you don't know enough about it to write something coherent.