Questions about public prayer

The current furore over public prayer in the UK seems to me to expose some of the key misunderstandings about religion prevalent in our society.  Without intending to get into the substantive issue at all, it seems worth noting these two assumptions:

1. There is a category called 'religion', and all the different belief systems, communities, and movements which can be thus categorised are basically the same.  Differences can be noted, of course, and nobody is saying that all religions are literally identical.  But that they can be classed together and therefore should be treated the same seems to be a pretty deep assumption.  Everyone accepts some limitations on this - but I suspect would usually deal with this by re-classifying some movements as 'not religious', or not proper religions (cults, perhaps?).
2. Religion is essentially a private matter, and even when it is invited into the public sphere it is expected to remain a private matter.  The public sphere is assumed to be a neutral, secular space, into which people can bring their private faith so long as they accept that it will then be withdrawn without having altered the character of the public sphere at all.

It is worth interrogating both of these assumptions.  Pertinent to the current debate, for example, it might be worth asking whether there is a difference between inviting into the public sphere a religious group which is inherently territorial and expansionist versus a group which focusses its political ambitions on a community which is not co-extensive with any state or territory.  I'm not saying you definitely shouldn't invite the first group; I'm just saying that prayer from these two groups would have different content and different connotations, and would have different implications for the nature of the public sphere.

It would also be worth considering whether the kind of benign secularism which governs the idea of the neutral public sphere is workable in practice.  What if that sort of pluralism was actually - as I would suggest it certainly was - the historical outworking of a particular belief system?  In other words, what if it never was value neutral at all, and what if attempting to make it value neutral actually leaves it more vulnerable?  And all this is assuming that a neutral public sphere is even a desirable thing, which I think needs some argumentation.

Finally, just to note that I've seen some Christian figures voicing a commitment to religious pluralism in the public sphere which I can't help thinking is theologically and politically naive.  Maybe it is just that I haven't seen the working behind their conclusions.  At the very least, I'd say we'd be wise to tread very carefully here.