First of all, thanks for reading! And yes, I do take the point that discussion requires disagreement; it'd be an awful old world if everyone thought exactly like me.
So, speaking as an American, I can assure you that there is no happy path where everyone suddenly becomes perfectly happy to live with their neighbor and you put the issue to bed forever. So let's take that as a starting point: multiculturalism, along with every other good thing in the world, requires perpetual work. And it requires work along a number of different paths.
One path is working to see society in terms of ideals, as opposed to physical traits. There's a lot to unpack there, but the core idea is that a lot of nationalist philosophies frame a society in terms of a particular trait - white, Christian, descended from someone named McGreggor, whatever - as opposed to a set of ideals - desire for freedom of speech, desire to live in peace, desire to be able to start a business, etc. A nationalist society will almost always fail at multiculturalism because they're focused on what a nation looks like, whereas a multiculturalist society focuses on what people DO.
And on that point, there are a few things that we have to accept in terms of minimal and maximal degrees of assimilation. One of those things is that there has never been any history of an immigrant community that assimilated fully into a society in less than a generation. Immigrants almost always live in somewhat segregated communities if they arrive in any large volume; it's easier that way. It's hard to learn a new language, hard to learn new ways, and people like a support structure. They also almost always maintain their own religion (isn't that the point of freedom of religion, after all), and that religion almost always has some conflict with the local religion.
The important thing to remember is that you don't need the initial wave of immigrants to adopt every single facet of the host culture all in one go. They only need to meet the minimum requirements to avoid getting in trouble - follow the law, pay taxes. Because they're not really the targets for assimilation. Their children are.
I'm reminded of the Irish in America. Back in the 1800s, people were worried that the Irish would never leave their insular communities, and would spread their heathen Catholic ways over the land, washing away the good Protestants. And... they assimilated in the space of two generations. That pace of assimilation has only quickened in the modern era, with lovely things like telecommunications to get messages into people's ears more quickly.
Which brings us to the second path - education. It is important, always important, for a society to educate its citizens about its ideals. This is something that America has been uniquely good at for years; land of the free, home of the brave, come here and do whatever you want. The message takes. We still have insular communities, but by and large our immigrant populations come here, settle down, and then within a generation their kids are speaking with LA Valley accents and running for Congress on their own xenophobic platforms. I joked in a different response, but only slightly, that within another twenty years we'll have some Congressman named Mendez loudly bemoaning the influx of those dirty, dirty Swedes.
And this is the second part of education - it is always, always important for any tolerant society to acknowledge and educate that tolerance means that not everyone has to integrate at the same pace, so long as they follow the law. An insular community does not harm the nation in any real sense. We've had the Amish in the US for a hundred and fifty years. No one cares. They're weird, their religion is mildly repressive, they have cultish tendencies, but we get on with our lives and they get on with theirs. Part of being multicultural is learning to live and let live.
Which brings us to our third path. Every nation in history that experiences an immigrant influx has had some demagogue stand up and start spouting some version of the Blood Libel - that community eats babies, that group won't assimilated, those people's religion is toxic, those folks' ideology will subsume our own. And they are universally wrong, historically speaking.
So part of being multicultural is to work to remember two things: One, dominant cultures almost always win, so don't worry about it too much. The most likely outcome is that you end up with a new food style and maybe a new holiday. And two, as with any exercise in combating racism or xenophobia, remember that there is a difference between the actions of the few and the response of the many. We have Southern Baptist preachers in the US who fulminate every Sunday about how everyone who reads Harry Potter is going to hell. And yes, from time to time a school district has to fight off an attempt to ban the book. But for the most part, those preachers' parishioners nod, smile, and then go home and read Harry Potter.
It's a trap to assume that everyone thinks the same way, even in an insular community. People are all generally motivated by the same desires: live well, make money, promote your family, don't get in trouble. If you expect everyone in an immigrant group to follow the directives of their most vitriolic leaders, you will be disappointed... in a good way.
Last but not least, a big part of being multicultural is working to realize that culture is never static. Even with any immigrant influx, culture changes all the time. That's part of life. Your children will not live in the same culture you do, no matter what. So don't worry so much about culture changing, worry about guiding it in a positive direction. I would argue that a positive direction is one that removes racist and xenophobic rhetoric as much as possible.
This is really an article all to itself, but hopefully that gives some indication of the direction of my thoughts on the subject. Thanks for reading!