Writing in the Australian context Tim Soutphommasane puts forward what he takes to be the defensible meaning of multiculturalism:
As social reality, multiculturalism simply describes cultural diversity as it exists in society. As public policy, however, it describes a set of approaches to settlement and integration for immigrants. It reflects the view that a society is better off taking active steps to welcome immigrants as future citizens, and accepting that a national identity will evolve over time.
[L]et's look at what multicultural policy in Australia has actually meant. Contrary to some suggestions, the policy has been clearly defined for many decades. Australia and Canada have long been considered leading examples of a successful citizenship model of integration.
The central idea is this. While we shouldn't demand new arrivals discard their cultural heritage, we should expect they become Australian citizens over time.
But any right to express one's cultural identity comes with the responsibility to accept our parliamentary democracy, the rule of law, equality of the sexes, freedom of religion, and English as the national language.
Tim adds that multiculturalism isn't the same as 'wishy-washy relativism'. Notice what is clearly implied by the above characterization regarding other possible meanings of multiculturalism. Tim's concept of it specifies constraints - rule of law, equality of the sexes, etc - on cultural diversity, and the implication of these is that individual rights prevail over cultural difference where there is a clash between the two. Multiculturalism, on this understanding of it, doesn't mean that anything goes only provided there is some tradition behind it.