At the same time women are putting on the headscarf, they are also going to work, to education, increasingly vocal in the media - and this is the confusing thing about Muslim women in the West,. They are becoming Westernized at the same time as they are adopting their religious identity more strongly.
To challenge the dominance of identity politics, we need to champion an alternative universalist approach. This wouldn't mean bland similarity, with everybody talking and looking the same. Instead, it would help us challenge the imposition of formal, ethnic categories and allow us to develop richer differences based on character and interests.
Some Muslim lobby groups have argued that Christian groups already have public funding for their schools and services so they should too. In response, there are now Hindu and Sikh organisations demanding their own concessions lest they feel left out. The demand to wear the headscarf one day spurs the demand to wear the crucifix the next.
Some people think that culture is overhyped and peripheral. A season of opera is less important than the refurbishment of a school, they say. Leaving aside the poverty of imagination and aspiration implicit in such a sentiment, it also ignores hardheaded economic reality: Britain, and London in particular, makes big money from culture.
Of course, when people work together, there can be tension and disagreement. But policing informal behavior makes it hard for people to speak freely for fear they will say the wrong thing. Even self-aware individuals can doubt their judgement and start to rely on the diversity trainer to judge if something is offensive.