I’m not sure about the cultural tool argument - the phrase normally implies cuturally specific tools . Perhaps what you are describing is the spread of western cuture through globalisation rather than any pre existing ability to become “liberal”.

True, although if one is realistic and accepts that migration will take place (both ‘aliens’ coming in, and ‘natives’ going out), then surely multiculturalism would seem more sensible to the conservative eye? If not, then they’re asking others to behave differently from how they themselves would behave.

I would also question your claim that liberal democracy is a part of “their” ie. migrant cultures - unless the migrant is from a post industrial, western society.

Two points to mention here. The first is to ask at what point ‘Liberal Democracy’ ceases to become the sole preserve of the West. For example, India has a pluralistic society that is democratic and becoming increasingly tolerant. I would say that this has been a part of Indian culture, at least since Independence, and probably before. Likewise with the Far East, Africa and the America - indeed, pretty much much everywhere except places like Saudi - where the concept of tolerance and democracy are political ideals in good standing (even if in practice, their governments might not live up to this ideal). In such cases, the immigrants already have the cultural tools they need to exist in Western Democracies, even if they choose to wear a sari and associate mainly with other Indians.

Second - Yes, many immigrants are from post-industrial Western societies. This is increasingly true since the restrictions on EU immigration were dropped. Multiculturalism is as much about celebrating Spanish or Polish culture, as it is addressing the complaints of hardline Islamic Fundamentalists. Maybe more so, since there are more EU immigrants in the UK, than members of Hizb ut-Tahrir.