Jonathan Haidt uses exactly this example in his research on what he calls 'moral dumbfounding', discussed here: What’s the Matter With a Little Brother/Sister Action? in Psychology Today.
Here are a couple more examples, that we have discussed here:
How do ethicists tackle the question "Is it immoral to have sex in public places?" Is it possible to use rational and empirical ideas to answer?
Is artificially generating images of minors in sexual positions unethical?
The TLDR is, we hijacked fear and disgust for social purposes, and they allow rapid reprogramming of societies by feedback about living successfully, that we call: culture.
The sex-in-private thing is a really clear example. We so take it for granted that it's an act that needs privacy, that it's fairly shocking to find we are one of only two species on Earth known to have this preference. But it's fairly easy to see from game theory arguments, that it greatly helps humans to cooperate to have the preference. So, socially programmed intuition.
We know from Hume that you can't 'get an ought from an is'. We don't reason our way to our morality. We have feelings what is right, then we use reason to justify and tune that, and decide how to act. Research on cognitive biases and post-hoc reasoning shows that this is how we do all our reasoning, unless we take special steps or systems we have developed to correct ourselves.
Haidt's research into how humans actually undertake moral reasoning in practice, led to Moral Foundations Theory. Lots of interesting conclusions follow, like feeling under threat as a teenager eg by pandemics or border conflicts, makes people tend to be more conservative for life, and less tolerant of ambiguities.
To get at the problems with legalising consensual incest, I'd draw comparison to the issues around legalising euthanasia. Every broadly agrees on what the risks of harms are, hardly anyone agrees about how or whether they can be managed, and public policy around the world varies wildly. Consider the wide variation in penalties for incest, and even definition such as whether cousin marriage is legal, as comparison.
Edited in response to comment
I hadn't properly understood the rating system of the Wikipedia page I linked to about variation in prosecutions. Same sex consensual adult incest is legal in Germany & Ireland. Legal full stop in Belgium, Argentina, Brazil, China, Israel, Ivory Coast, Latvia, Japan, Lithuania, Luxembourg, Philippines, Portugal, Russia, Serbia, Slovenia, Spain, South Korea, Thailand, & some US states. 20 out of 192 countries. That covers jurisdictions with approximately 1/3 of the world's population. Many more like India don't have specific prohibitions, likely leading to uneven persecutions, and casting doubt on the idea it is a universal cultural taboo or surely it would have been codified into law early on. Honestly I think this challenges the basis of my argument. It would be interesting to find research about any tensions between social pressure/condemnation and the law. Same-sex consensual adult incest is an even clearer example for discussion, because there is zero risk of offspring - it perhaps also challenges reasoning from intuition even more directly, adding unease many feel but can't justify logically about homosexuality. Bigger than the questions about moral behaviour here, are questions about the role of government and when intervention in private lives is permissible.
I would look to the history of prohibition of incest. Greece has some of the oldest records regarding it. Many stories in Greek mythology are about kings who could literally do anything they wanted, like Midas, and Sisyphus. Oedipus was blamed for a pandemic that struck Thebes, which the Oracle at Delphi said resulted from the killer of the previous king - leading Oedipus to find that was him. Greek mythology has the Erinyes or Furies, deities of vengeance that punished 'the crimes that most offended the gods', regicide, killing family, and murder, by hounding those that committed them to madness. We can understand this now as guilt, and maybe PTSD. Orestes was a just king, but his crimes to get there meant he could not be free of the Furies. Incest was likely to result in abnormal births or stillbirths, interpreted as judgement by the gods (the Minotaur is another example of a probable abnormal birth, interpreted as a judgement). We should see that judgement as not on a single case, but as on a social tolerance of incest, because multiple generations committing incest gigantically increase the risks. We can see this with the results of Habsburg cousin-marriage, especially in Charles II of Spain, child of an uncle and niece marriage.
The powerful have many times denied the hold of laws about incest over them. But social condemnation, and conscience, and the feeling they and their lineage were facing the wrath of the gods led to a cross-cultural sense that incest was worse than a crime, it would lead to being cursed.
We begin our moral reasoning with our intuitions, that is inevitable. Our intuitions come from game-theory dynamics, encoded into culture. We have a deep intuition incest is wrong, and cultural guards against beginning to tolerate it, because the impacts are cumulative, eg one case might be consensual, but tolerating incest in general makes cases with bad power dynamics more likely, and compounds genetic damage. Our societies are not ordered by accident, we can look to the idea of Moral Foundations Theory to understand that holding certain core values is key to humans collaborating. And I would say tolerating incest, even consensual sibling incest, directly challenges these sources of social cohesion (specifically Care & Sanctity).
Given wide cultural variation in prohibition of consensual adult incest, it seems wrong to say 'deep intuition incest is wrong, and cultural guards against' is a cultural universal. There is cultural variation in whether natural disasters are a judgement, so perhaps cultural framing is key. Maybe also how hierarchical a society is, with Habsburg gene-flow into the wider population being pervasive and very widespread, the impact of their inbreeding preference was more damaging. Maybe other factors about experiences of negative impacts of incest should be considered, like in Judaism where marrying within the religion was strictly enforced in relatively small communities, the Torah prohibitions against incest only cover Jews not gentiles (and men not women, Sodom was about abuse of strangers through explicitly treating sodomy as a violation of male power, a widespread concern only in highly patriarchal cultures). Looking at these together, it would be interesting to look at whether incest prohibitions relate to social inequality when the law was passed, as in unequal patriarchal societies the impacts of incest would be concentrated and affect populations more.