Liberalism prides itself on its toleration of cultural and other differences. Some cultural groups, however, are internally illiberal. They do not treat their members as free and equal autonomous individuals with rights but as having identities defined by their membership in and place within the group, and by relation to the group's values. They are communal selves rather than individual ones. People so identifying themselves cannot easily flourish in liberal society by taking advantage of its freedoms. Hence, it is said that liberalism cannot treat such minority cultures fairly in accordance with its own principles.
Liberalism can tolerate such groups provided that they do not harm others and provided that their members are free to leave without suffering unjust discrimination. The problem is whether persons formed in such groups are really free to leave unless they have had a liberal education that enables them to think of themselves as individuals with the power and right of choice. But if they do think of themselves in this way, they will no longer be the communal selves they were. The liberal education of its members would undermine the group's illiberal identity and force it to reconstitute itself in liberal terms. It is clear also that illiberal groups could not be specially represented in the political realm without turning that realm from a principled association into what would be at best a pragmatic compromise between conflicting groups. There is no reasonable compromise between liberalism and illiberalism. In the end one must seek to show the superiority of a liberal society by appealing to some foundational principle and by reiterating that there is no possible social scheme compatible with a principled order that is more tolerant of difference than liberalism.
A more modest claim for the special recognition of cultural difference would be that of cultural minorities whose values are not incompatible with liberalism but whose members are disadvantaged relative to the majority in terms of their ability to compete on fair terms to obtain the benefits of liberal society. The demand would be in part for the preferential treatment of the members of such groups so that they could enjoy fair equality of opportunity. But this would not be to give special recognition to the culture as such but to its members as disadvantaged individuals. Some cultural minorities might also reasonably claim to be given symbolic public recognition as distinct and loyal members of the polity in public ceremonies celebrating the history of the nation and the contributions of its various citizens.