I think that's 100% true about skin colour. But that's not what this is about - it's about integration.
Most communities in the history of immigration have had, for different reasons, a drive to integrate. I think that is not the case currently and that's critical.
Our culture and society is probably now more welcoming than it's ever been to immigrants who want to be British*. I think most people are not default, unashamed racists anymore, as they were in the 70s and 80s. I absolutely know that institutional racism, micro-aggressions etc still exists, but broadly speaking your average white Briton who has been through the school system is much less likely to use racist slurs for example, or to express hostility to second-generation incomers on the basis that they aren't white. It's not enough - but it's meaningful in the broader context of what is going on now.
What is happening now is a response to a lack of integration. I, a lifelong leftwing feminist, feel it myself. I don't like groups of men gathering to smoke on the corner of my street while the women are invisible after school pick up time. I don't like seeing six-year-old girls in restrictive clothing which makes it impossible to run and play, while the boys do so freely.
I don't like the fact that multiculturalism has prioritised the 'cultural sensitivities' of the male authorities who preside over those cultures, and not the human rights of half of that culture. I don't like the 'don't tell Muslim women that their choices are invalid' narrative that asserts that, magically, those deeply patriarchal cultures are the only ones where social pressures, internalised misogyny, and fear of retribution don't impact those 'choices'.
I especially don't like the fact that it is now pretty much impossible to say so publicly in the liberal-but-privileged circles in which I live and which run the country at most levels. [As an aside, I am not liberal myself - I'm far towards the radical wing of both leftism and feminism and believe liberalism has been the smiling face of the globalised capitalism that is about to destroy us.)
I know that my position is probably unusual - I doubt that many people calling for limits to immigration are doing so because they are concerned with women's rights. But I think what I experience - a sense that there is a growing portion of our society which is actively and openly hostile to what we call our 'common values', however poorly applied and fractured those values are, however far we have to go before those values are actually structural in our society - is very, very common.
That sense of a rejection of common values can be about ideology or politics, or it can be as simple as 'the men gather on the street corners to smoke, and they pretend I don't exist so I have to step into the road to pass, and the women are inside' or even more simply 'multiculturalism has somehow caused a whole area is mono-cultural'. On the latter point, you can indeed argue that people somehow didn't have a problem when the monoculture is White British - but it's nevertheless insane to pretend that it's not basic human psychology to notice when an incursive group takes the geographical place of the previous group.
Most of the people who are expressing a profound unease at where we're at are able to do so precisely because they are not in the liberal-but-privileged class. They don't have the vocabulary or political sophistication to articulate the nuance of what they feel, so it gets expressed through the language of a retrogressive racism which I don't think they actually feel. Or perhaps, the overt expression of racism has been more recently accepted for them than for privileged liberals, so that language bubbles back more quickly.
But we are idiots if we pretend that it's not a problem.
Doing so alienates the people who still form the majority of this country, and who, if they lose faith in the flawed project of liberalism, could fuck everything, for all of us. Because while liberal govts pretend they can't hear them, anyone who has an interest in harnessing their rage pretends they can.
*while retaining their distinct heritage.