Few issues have divided the Coalition as dramatically as the question of how to meet the threat of home-grown Islamist terrorism. One group of ministers – which includes David Cameron and the Education Secretary, Michael Gove – advocate a radical new approach based on confrontation. They argue that all official engagement with groups that promote a message that conflicts with "mainstream British values" should be broken off. Such organisations, they argue, should be ostracised in the same manner as far-right groupings such as the National Front. Drawing on the analysis of the Quilliam think tank, they see a clear link between intolerant attitudes within the Muslim community and support for terrorism.

Another group of ministers – which includes Nick Clegg and Baroness Warsi – reject the idea that there is a connection between reactionary religious attitudes and support for terrorism. They argue that there needs to be a rigid separation between official policies designed to promote community cohesion and policies designed to disrupt terrorism – and that the approach of the first group of ministers conflates the two in a dangerous manner. This second view is reportedly shared by some influential figures in the intelligence services, the police and the civil service. And it was also articulated by the House of Commons' Communities and Local Government committee last year.

The two groups have been battling it out for control of counter-terrorism policy behind the scenes for many months. But the first faction has now, apparently, prevailed. The new "Prevent" counter-terrorism strategy, published by the Home Secretary, Theresa May, yesterday leans strongly towards a confrontational approach. It explicitly aims to widen its remit to the elimination not only of support for violence, but also of ideological extremism. Ms May says Home Office funding will be withdrawn from all organisations that "do not support the values of democracy, human rights, equality before the law, participation in society". She has also demanded a more intolerant line from universities and prisons with regard to the activities of Islamist groups on their premises.

It is plainly foolish for the state to be funding groups that promote intolerance. And the previous government's belief that radical groups could be used to steer individuals away from violence was indeed naïve. But breaking off contact with all groups that expound unpalatable views (and stigmatising the forums in which they, and other groups, might speak) is not sensible either. The way to deal with intolerant views is by confronting them in open debate, not silencing them.

There is a further problem. Earlier this year Baroness Warsi thoughtfully outlined the dangers of dividing Muslims into "moderates" and "extremists" based on their religious beliefs, as opposed to their attitudes towards violence. The obvious implication of this division is that, in the eyes of society, the less devout a Muslim is, the better. This risks stigmatising not only extremist Islam, but Islam itself.

There are also dangers in treating British Muslims as a "terrorist" problem. This is liable to result in further alienation of sections of the community. Research conducted over the past decade suggests that terrorism arises where alienated individuals come together with a legitimising ideology and an enabling community. The danger is that the confrontational approach now favoured by the Coalition will not drain the swamps of extremism, but help to fill them.

Ms May argued yesterday that the new strategy will prove more effective in eliminating the scourge of domestic terrorism than the one it replaces. Much depends on how carefully it is implemented. But on first inspection, it looks more like a step backwards.