Firstly, on social integration, schools in particular have a strong interest in encouraging integration and tolerance as strongly as they can. There are plenty of studies showing that diverse and integrated student bodies are more successful, academically and in other ways. This is especially true for minority students and goes right up to the college level. It's why colleges actively fight to keep affirmative action programs legal; the programs let them encourage diversity to the advantage of all students.
I'd argue that companies often have an equally strong interest in reflecting the community that they serve and being as open and accepting as is humanly possible to exclude as few customers as they can. Part of this is political correctness, which is simply acknowledging things that do or can offend people and avoiding doing or saying them in front of others. 99% of it is just awareness of what is (or may be considered) a slur or rude. 1% is stupid nonsense utterly unrelated to any real concerns. As far as I can tell, much of that 1% is bullshit made up by British tabloids to mock political correctness.
America isn't really even multicultural, it's monocultural. It's a 'melting pot', not a 'cultural mosiac'. I'd think the goal is to intergrate other cultures into our own, rather then enforce several distinct cultures in the same country.
Except that this is blatantly false. There is no one American culture, even if you discount all racial minorities.
Within America there are more distinct cultural traditions than you can comfortably list. Compare New England to the mid west to the deep south to the Canadian border to California to Texas to Hawaii to DC to Las Vegas to NYC to Boston to San Francisco to to to... The mosaic may not be divided on (solely) racial lines, but it's obvious that one exists. And within that range of cultures it's often hard to point to any common, let alone defining set of features and say that that is American culture.
It's probably why politicians who like to use the idea of an American monoculture have to keep dividing the nation into 'real' America and all those messy, culturally diverse places where people might notice that the monoculture only exists in their heads.
You see the same here in Britain. The very people who like to talk about Britishness are the same who, in another context, will happily play up the cultural difference between cities, counties, the north and south, or at least the different countries on the island. The idea that we can't accept some level of outside culture in that mix is absurd to me. And this is in a far smaller and less racially diverse nation. As far as I can tell, Britishness is the face put on for other nationalities when you want to play on their stereotypical views for your own advantage. You drink the tea and let the accent ring (whatever that accent might be) and instantly acquire essence of *insert current British film star/character here*. Or not.
EDIT: I should just say, multiculturalism tends to mean very different things depending on who is talking. I tend to avoid using the term it simply because that semantics fight is a distraction and lets people avoid the actual topic, but not having that fight means people just talk past each other by saying that what the other person is saying isn't actual multiculturalism.