Multiculturalism argues 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. Individual autonomy requires a societal culture supplying meaningful options; minority cultures cannot always sustain one unaided; so group-differentiated rights are a requirement of liberal equality and not an exception to it. 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 instead of 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. A politics of equal dignity that 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. A universal citizenship asking 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 attack from two directions since. Liberals and republicans hold that entrenching group identity fragments common citizenship. Feminists note that the cultures being protected often subordinate their own women, Susan Okin's "Is Multiculturalism Bad for Women?" being the sharpest statement of it.