I don’t think that you deserve downvotes for this because I don’t think you’re necessarily incorrect. I do absolutely feel cognitive dissonance here. I have a visceral, what I think is instinctual, revulsion at the concept of incest. But, if there is love, consensuality, and no one is being harmed (including possible offspring), I cannot in good conscience say that they do not have a right to be together, regardless of how I feel. It takes overriding that feeling to state as such, which isn’t comfortable and is, by definition, cognitive dissonance.
I do not, however, think that the comparison to homophobia or other discrimination against LGBTQ+ people is a good comparison. The majority of relationships that LGBTQ+ people engage in are consensual and do not cause harm to anyone. The majority of cases of incest involve sexual abuse and frequently pedophilia. Offspring of close relatives are at high risk for significant biological and social harm (in cases of abuse add psychological harm).