Multiculturalism is the argument that liberal neutrality is not available, and that pretending otherwise disadvantages exactly the groups it claims to treat equally.
Its starting observation is that no state is culturally neutral. It conducts business in a language, keeps a calendar with particular holidays, teaches a history, and recognizes certain forms of marriage and property. For the majority these are invisible defaults; for minorities they are the majority's culture presented as the absence of culture. Kymlicka drew the liberal conclusion: since individual autonomy requires a societal culture supplying meaningful options, and minority cultures cannot always sustain one unaided, group-differentiated rights are a requirement of liberal equality rather than an exception to it — and he distinguished sharply between external protections, which are legitimate, and internal restrictions on a group's own members, which are not.
Taylor made the case in terms of recognition rather than autonomy. Identity is formed dialogically, so misrecognition — being reflected back a demeaning picture of oneself — is a real harm and not merely an absence of respect. The politics of equal dignity, which treats everyone identically, therefore sits in genuine tension with a politics of difference that asks for what is distinctive to be acknowledged.
Young attacked the ideal of impartiality itself, arguing that a universal citizenship which asks people to set aside their particular identities in public has always in practice asked the marginalized to adopt the perspective of the privileged.
The tradition has been under sustained attack from two directions since: from liberals and republicans who hold that entrenching group identity fragments common citizenship, and from feminists — Susan Okin's "Is Multiculturalism Bad for Women?" being the sharpest — who note that the cultures being protected often subordinate their own women.