Ancient taboo
Most "liberal" modern societies were not created liberal, but rather emerged in the last couple of centuries from the societies that were very traditional and religious for millennia. Thus, liberalization of various aspects of life, especially those related to sexuality, is very gradual and depends on slowly evolving public opinion, rather than on whether this or that aspect of life corresponds to the formal liberal canon. In this sense, the emancipation of women, sex out of marriage, and legalizing homosexuality are all rather recent developments.
Interdiction against incest is arguably very ancient, perhaps even predating human culture and consciousness - because they are grounded in biological disadvantages. Sigmund Freud in Totem and taboo discusses complex caste and tribal systems preventing interbreeding with kinship dating several generations back, which exist in what one would consider otherwise primitive cultures - notably in terms of their lax attitudes towards homosexuality and marriage (especially monogamy.) One could even argue that many social animals avoid incest, since it confers a biological disadvantage on the progeny.
This interdiction only partially makes sense in the modern society, since incestuous couple may not necessarily wish to have children. (Moreover, they may be homosexual or simply in-laws - although such situations are usually not criminalized, they might still be negatively viewed by the society.) One could also cite more modern methods of avoiding incest, developed in societies where close kinship is a real problem, e.g., App to prevent 'accidental incest' proves a hit with Icelanders or genetic testing to prevent well-known hereditary anomalies, like Tay-Sachs disease.
Conflict with other liberal values
A big issue with incestuous relationships is that they happen among the family members, where the relationships are hidden from the rest of the society, and the power dynamics might be very different from that among strangers, or even supported by law - like the power of parents over their children. This opens multiple possibilities for abuse. While prohibiting incest doesn't address the core of the problem, it provides an easy way of punishing the abuse that is otherwise hard to prove.
The highly publicized incest stories often concern siblings who have grown separately and may not even be aware of their kinship, but decriminalizing incest potentially implies dismantling the corresponding unspoken interdictions for sexual relationships between parents and children or siblings growing together.
Is marriage liberal?
One could also ask a broader question: whether a liberal society needs ancient institutions like marriage, which are ultimately grounded in a religious practice. Notably, many socialist and communist utopias suggested abolishing marriage, in favor of freely intermixing of sexual partners, and raising children together. In this sense the fight for "gay marriage" might have been going in the wrong direction - by strengthening the very institution which is the root of the problem.
Civil union in Israel
An interesting example is Israel, where the marriage was outsources to the religious authorities from the moment when the state was established, which meant that only the recognized members of the same religious group could be married (by a representative of the same religious groups, such as a priest, rabbi, imam, etc.) This was seemingly discriminative of the couples with no religious affiliation or inter-religious couples. The state however had to deal with the reality of such couples, the couples married abroad, and the couples formally unmarried, but having children. This resulted in gradual emergence of legislation and court rulings that give rights to such couples in terms of taxation, visitation, inheritance, visas, etc. Today non-religious couples may get married abroad (with nearby Cyprus being the most common destination) or simply secure a proof of living in a common household (e.g., by having common property, paying bills together or arranging for an official declaration of such an intention at notary public.) In this context the legal recognition of the same sex couples was a seamless process, despite the religious marriage being impossible for them.
Civil union in France
Another example is the Civil solidarity pact (PACS) in France. Although the traditional marriage in France has been non-religious for a long time, until 2013 it had been restricted to heterosexual couples. As an early measure civil union was promulgated in 1999, giving same-sex couples a measure of legal recognition by the state. Surprisingly, the measure turned out to be hugely popular between heterosexual couples, unwilling to burden themselves with traditional expensive and time consuming marriage/divorce arrangements, but willing to guarantee a measure of legal protection to themselves and their children. As the results the number of couples entering PACS is nowadays nearly as big as the number of couples registering in an official marriage. (It is worth noting that PACS is open to any pair of individuals functioning as a common household - even if they are not engaged in a sexual relationship.)