The main biological reason against inbreeding is that, since close relatives have highly similar DNA, it means that the DNA of the child is almost exactly the same as that of the parents. This means that any genetic defects in the family are likely to remain in the family, including those responsible for hereditary illnesses and pathogen vulnerabilities.
However, a sufficiently advanced race could have found a way to induce certain genetic changes during the gestation period, meaning that 2 relatives can produce offspring while still giving birth to a sufficiently different offspring. Already, humanity is getting there, with in-womb genetic testing and use of viral-based delivery methods for genetic code.
So once the genetics are out of the picture, the only hindrance is the social taboo. Already, there are communities like certain rural areas of Southern US states like Alabama where first cousins can marry and procreate. And even in western Europe, it's estimated that 1% of new marriages is between first cousins. It wouldn't be the first time that social taboos get broken, as happened with interracial marriages in the 1960's-70's and gay marriage in the past decade. In fact, back during the classical eras of the Romans, the Greek and the Ancient Egyptians, there was no such taboo. For example, Tutanchamon was married to a half-sibling.
There are not really any benefits to large-scale incest, though, especially in a science-based world. A genetic trait would be distributed far better through an air- or waterborne pathogen. In fact, incest would be counterproductive to spreading a trait, because you want to spread the trait to as many family trees as possible.
However, on a smaller scale, incest can enhance traits found in a small subgroup of a society. The only reason this would be acceptable, though, is if there is only one family with this genetic trait, which is rarely the case. usually, due to the natural resistance against inbreeding, any genetic traits formed through chance mutations during conception are present in multiple families.
Finally, fringe groups in society might naturally distrust people that aren't part of their small group, and would eventually have to start performing incest to keep the group population big enough.
Another reason that incest might be performed is for adult entertainment purposes, but those almost never result in offspring. In fact, as long as there is no offspring from the act, incest might not be viewed as a big social taboo.