The Archbishop of Canterbury's speech contains a passage that I thought worth quoting separately from my broader discussion below:

The grounds for legal restraint in respect of language and behaviour offensive to religious believers are pretty clear: the intention to limit or damage a believer's freedom to be visible and audible in the public life of a society is plainly an invasion of what a liberal society ought to be guaranteeing; and the obvious corollary is that the creation of an offence of incitement to religious hatred is a way of avoiding the civil disorder that threatens when a group comes to feel that it has been unjustly excluded. Since the old offence of blasphemy --- as we have seen --- no longer works effectively to do this, there is no real case for its retention. How adequately the new laws will meet the case remains to be seen; I should only want to suggest that the relative power and political access of a group or person laying charges under this legislation might well be a factor in determining what is rightly actionable.

Later on, the Archbishop echoes this legal point (though in a passage that chiefly focuses on moral questions):

The assumption of the naturalness of one's own position is regularly associated with an experience of untroubled or uninterrupted access to the dominant discourse and means of communication in one's society. If I can say what I like, that is because I have the power and status to do so. But that ought to impose the clear duty of considering, when I engage in any kind of debate, the relative position of my opponent or target in terms of their access to this dominant means and style of communication --- the duty which the history of anti-Semitism so clearly shows European Christians neglecting over the centuries. I have intimated that I think the law could and should take this into consideration where 'incitement to hatred' is concerned; but it is again primarily a moral question, the requirement in a just society that all should have the same means to speak for themselves.

Lovely: First, "language and behaviour offensive to religious believers" should be suppressed when they are "inten[ded] to limit or damage a believer's freedom to be visible and audible in the public life of a society" -- and of course the "limit or damage" stems from the message the speech communicates, not just (say) the physical noise created by the speech (which may physically keep people from being "audible"). But, beyond this, whether such "language" is to be punished should turn on "the relative position" of the offended religious believers, presumably relative to the speaker.

So I take it, in a magnanimous gesture, the Bishop of Canterbury would offer himself and his Established church less protection when it criticizes (if it ever does) Islam than Muslims would get when they criticize Anglicanism. But what if a Muslim apostate criticizes or insults (or both) extremist Muslims, or for that matter mainstream conservative Muslims? What if a Muslim criticizes Jews? What if an atheist criticizes Muslims, or vice versa?

And of course, as we know, different groups have different "relative power and political access" in different contexts. In much of America, atheists and even, more broadly, secularists have less power and political access than Christians generally or even conservative evangelical Christians in particular. But in some towns and on many college campuses, the matter might be different. I imagine there are similar differences within England. I take it then that an atheist's "language and behaviour offensive to [conservative evangelical Christians]" would be protected against criminal punishment under the Archbishop's proposed blasphemy law in most places, but not on college campuses where the "relative position[s]" are reversed.

What about "relative power" that stems not from political or financial influence, but from a willingness to use violence? If many critics of Islam are intimidated by the risk of violence from Muslim extremists, does that mean that a Christian's criticism of Islam would be protected because Muslims have more "power" to intimidate stemming from some Muslims' willingness to use violence -- or unprotected because the Muslims have less "political access" than the Christians?

Finally, the Archbishop's proposal gives supposedly low-power groups a quite remarkable sort of power -- the power to use government machinery to suppress "language and behavior offensive" to them, while their adversaries lack this power. How does that change the balance?

A pretty poor proposal, it seems to me, on many levels. But unfortunately it's the sort of poor proposal that many groups find appealing, in particular out of a misguided sympathy for the supposed underdog that leads them to undermine both liberty and equality.