Answer: "Multiculturalism" is a word that is used for two rather different social movements.
On the one hand, it stands for the recognition that human beings are all fundamentally equal, regardless of ethnic background, and that there are many fine things to be found in cultures all over the world. This movement can be seen as an attack on European ethnocentrism, but fundamentally it follows from the ideals of the Enlightenment. It is entirely consistent with a philosophy of reason and individualism. Not everything about Western Culture is glorious (Ayn Rand, after all, saw herself as standing against many of the main threads of Western thought), and not everything about non-Western cultures is inferior. Objectivists would not call this attitude anything other than what it is, fundamentally: individualism.
But "multiculturalism" also stands for a movement, prominent in academic humanities departments, that is fundamentally a philosophic attack on objectivity in epistemology and morality. This is the doctrine that simultaneously (and incoherently) propounds the equality of all ethnic groups, and stridently attacks all aspects of Western thought as corrupt (racist, classist, "logocentric," sexist, etc.). Objectivism
is absolutely opposed to this movement. In the first place, there are fundamental ideas that historically arose in the West that are both true and profoundly important. Logic, the scientific method, science itself, democracy, human rights, and more generally individualism are all of Western origin, just to name a few. There are many other aspects of traditional Western culture that stand the test of objective scrutiny, and not all non-Western cultural practices are superior. In fact, when it comes to philosophy, many non-Western ideas are just dead wrong (but then, so are many Western ones).
When academic multiculturalists attack logic or science as an ethnocentrism, when they decry capitalism and extol traditional peasant life, when they propound the equality of all moral perspectives (as long as they are GROUP perspectives), they are discarding the philosophic foundation that must exist for human beings to prosper on earth and in society with each other.
Logic is not an arbitrary social convention, like the choice between chopsticks and a fork and spoon. Logic is the art of reasoning correctly.
Science is not a tool of oppression, it is a tremendous body of knowledge that has liberated the average human being from bondage.
And not all moral systems are equal; moral reasoning must proceed on the basis of objective standards and an appreciation of the value-significance of individual life and happiness. The academic multiculturalist offers one type of tribalism for another; while the Objectivist (like people of Enlightenment values more generally) offers an answer to tribalism, no matter what its form.
Multiculturalism is not really about choosing non-Western clothes if you like, or listening to World-beat music, or about rejecting racism. That is individualism. Multiculturalism is an anti-intellectual movement that promotes group-think to cure racism, denies truth to avoid facing facts, and rejects human rights and morality in the name of humanity.