There is a gulf in understanding between those who follow "interest group politics" and those who identify with the larger tradition they belong to.
The leaders of minority groups often understand that in a liberal society the aim of politics is to create a formal structure through which self-interest can be equally pursued (with the formal structure including definitions of rights). They see the aim of politics, therefore, as being to organise as a minority interest group and to make sure that this framework (of pursuing self-interest) is structured in a way that is biased for rather than against their own group. The minority groups will often assume that this has also been the focus of the majority, meaning that the majority has used its influence to structure society to its own benefit (hence the notion of majority privilege dominant on the left today).
White liberals who belong to the majority often perceive society the same way that minority groups do, and so tend to be sympathetic to claims of majority privilege.
But for most members of the majority all this is very confusing. They don't see their society as being a field of contest for competing rights. Their society means much more to them than this. It has a meaning as an entity in itself: as a source of identity, as an expression of the culture that is connected to one's own people, as a means of transmission of a distinct tradition.
Furthermore, the non-liberal member of the majority will want his society to be ordered according to objective moral truths, rather than being merely a system enabling the pursuit of self-interest.
So there is a seemingly unbridgeable gulf in understanding here. Unfortunately, the majority has to understand that it is liberal whites and minority interest groups who are running the show, so their understanding now dominates.
I have had readers in the past who have insisted that liberals aren't interested in the truth and that there is therefore no purpose in trying to argue with them logically. I've mostly disagreed as there do exist principles within liberal thought which liberals follow through to their logical conclusions.
However, I agree that liberals, in thinking about the nature of society, aren't as oriented to what is objectively true or good. Instead, they focus on relationships of power - on who gets to benefit from structures which limit or empower the pursuit of self-interest (when liberals praise someone for being "empowered" doesn't it often mean that the person has thrown off limitations in the pursuit of what they want?)
It should also be said that even though it is left-liberals who have made interest group politics their own, right-liberals did much to prepare the ground for it. It was right-liberals who pushed along the idea of society being made of millions of rights-bearing individuals each pursuing a rational self-interest. It was not a long step from that to the idea that the contest was not just between individuals but between interest groups.
So even though it's true that right-liberals often hate the idea of interest groups replacing individuals (with many complaints about the intrusion of ethnicity, culture and race into politics), it was right-liberals themselves who set up the idea of society as being a neutral or vacant space rather than a space that was already inhabited by a particular culture, tradition and people.