Interest groups

Several months ago, I came across a claim A C Grayling makes regarding the role of religion in public life. The claim seems sound, and yet it also seems radical. I am appealing here to my religious reader(s): is there a good counterargument?

Here's how he puts it in The Meaning of Things:

No doubt the churches are as entitled as any other interest group to have their say on matters that fall within their range of concerns, but they are an interest group nonetheless, with highly tendentious views, and big axes to grind. (p.104)

He makes the same claim in other places, including here and here.

Is the role of organised religions in public life on the same level as that of other interest groups (such as, say, the Royal Society for the Protection of Birds or the Calgary Chamber of Commerce)? Or is there a role that religions legitimately play in public life that interest groups cannot play?

I'm not asking about private life: I know that religious individuals get much more out of religion than out of their local gardening club, for example. I'm asking about the public role of religion in secular society. For example, is a religious holiday any different in kind from Earth Day, or Breast Cancer Awareness Month, or Darwin Day?

I think Grayling is right that there is (or ought to be) no difference in kind between religious and other interest groups (even Humanism), when it comes to their official status in the public sphere. Is this a valid assertion?

Archbishop of Canterbury Rowan Williams claims there is more to it, but fails to give a clear (or even coherent) argument for why this is so. Why should society at large (and the government in particular) treat religious lobbies as other than interest groups?