I can refute it in less than 500 words.
Take the culture of Nazi Germany or modern neo-Nazism:
The traits of Nazi German culture: racism, authoritarianism, anti-Semitism, homophobia, hatred of Roma gypsies, extreme Social Darwinism, and German racial supremacism.If you seriously think all cultures are equal in every respect, then it follows directly that you must believe that Nazi culture is absolutely equal to all other cultures today and in the past. This is insanity.
Let us take the ways in which cultures might be judged as equal:
(1) that the empirical propositions they hold are all equally true;There is no way you could rationally hold all these ideas about Nazi culture. Even on (3) it would fail, because aesthetic judgements are subjective to a great degree and so cannot always be equal.
(2) that they are all equal morally or ethically;
(3) that they are all equal in terms of aesthetic judgements that one could make about cultures or cultural beliefs.
Secondly on (1), certain empirical propositions in Nazi culture are plainly false. E.g., Social Darwinism is based on a spurious appeal to nature fallacy and the notion of German racial supremacism is not supported by the empirical evidence (e.g., even identifying a German “race” in the sense imagined in Nazi mythology in a meaningful sense is not possible because so many Slavonic peoples have assimilated to German culture over the past 1,000 years).
On (2), if one thinks we can have an objective ethics, then all cultures cannot be equal, because they often have radically different moral and ethical ideas. But even if you think morality is subjective or a matter of emotion, it also follows that all cultures cannot be equal in moral terms because they also have radically different moral ideas judged very differently by different people.
The only way that one could defend the idea that all cultures are equal is to defend the idea that there is no objective truth at all, and so all ideas or propositions in every culture are equal only in the sense that they are all true only in a culturally relative sense in each culture. But truth relativism cannot be taken seriously, and leads to utter incoherence and intellectual bankruptcy (see here and here). That route leads to intellectual Bedlam and cannot be defended.
But even the absurd Postmodernist defending the notion that all cultures are equal on the grounds of truth relativism would be refuted by (3) above (aesthetic judgements that one could make about cultures or cultural beliefs). As we noted, aesthetic judgements are so obviously subjective to a great degree and they simply cannot always be equal.
To conclude, none of this means that crude 19th century racism is true or that ethnic prejudice does not exist. In no sense does it follow that people are justified in irrational or unjustifiable prejudice or bigotry.
The recognition that all cultures or cultural ideas are not equal is intelligent, obviously correct, and actually one that all decent and compassionate left-wing people should uphold, for the world is filled with bad or incorrect cultural ideas that need to be fought.