Murky waters...
It's pretty obvious from the news coverage that some of the opposition to the Archbish's remarks are orchestrated by the evangelicals in the CofE determined to get him for anything in order to block his moves towards tolerance* of homosexuality.
Some of the rest of the opposition is founded in general uninformed racism.
So, what do I think?
One of the advantages of large-scale immigration is that the best of what immigrants bring from their culture can be incorporated into British culture to the benefit of all - this is most apparent in cuisine but examples abound elsewhere. I am insufficiently familiar with Sharia Law to know whether there are aspects that are worth incorporating into the British system, but if there are I wouldn't oppose it merely on principle. And certainly, there is an established tradition of local arrangements for arbitrating matters such as neighbour disputes, and if a Sharia system is acceptable to both parties, I see no obvious reason to oppose this.
There has been some opposition to allowing Sharia to be the basis of settling, for example, marriage disputes. All the evidence is that Islam, along with Christianity and other religions, exists merely to sustain patriarchy. In other words, secular society has worked to make the British system fairer to women, anything that moves away from that is wrong. If people don't like the way the British system works, campaign to change it. Campaign to persuade the majority of the wisdom of your way. Or shut up.
My concern about the Archbishop's view are deeper than that, though. Over the past ten years or so, there have been several examples of where the Democratically elected government has legislated to create a fairer society against the prejudices of the religious fanatics - the most obvious examples being on gay matters. The forces of organised Christianity still labour under a misconception that they are a suppressed group, discriminated against, despite the evidence to the contrary. They don't seem to understand, or understand but reject, that any laws against homosexuality make life intolerable for gays,whereas laws equalising homosexuality have no impact on the lives of those who oppose them.
We only have to look at the ridiculous row over adoption agencies, where the Catholic Church declared that its agencies which specialise in placing 'hard to place' children would shut down rather than 'be forced' to place children with gay people (thus demonstrating that they care less about child welfare than their sex obsessions). Although the Anglican Church doesn't maintain such a bigoted position with its adoption agencies (which must have come as a shock to many of its members), it supported the Catholic Church's right to practice mindless bigotry.
So perhaps Rowan Williams is actually trying to say that all religious organisations and its practitioners should have the right to set up a parallel legal system outside the bounds of civil society.
This could include, for example, rejecting any state 'interference' in state-funded religious schools (suspending the employment law against religious discrimination, persecuting employees whose sex lives don't meet their requirements, resisting attempts to implement a sensible and workable sex education policy, fear that they might have to accept pupils who live locally irrespective of their parents' religious practices).
I suspect some of the reactionaries and evangelicals would be less vocal in their opposition to Williams if they understood his agenda. Even so, many of them are opposed to any recognition of Islam, or any other non-Christian religion, because of their unshakeable conviction that their way is 'right' and any alternative is 'wrong' even though they are united in their hatred of women and gay people.
*As a by the by I hate the word 'tolerance'. It's entirely inappropriate for attitudes towards homosexuality. 'Tolerance' is something one does grudgingly - one tolerates various impositions as preferable to alternatives. One tolerates low-level pain because there is nothing we can do about it. One tolerates the tolerable because to demand better requires disproportionate effort.
