Here is Part 1
In a strict sense Christians don't worship the same God. From an epistemological viewpoint what we worship is our idea or understanding of God and there are as many of those as there are people. All that a human has access to as far as worshiping God is a participation in worship empowered by the Holy Spirit. Now since this is a general human condition there is no self-evident reason to limit or segregate this by sociological boundaries. If there are boundaries they would be set by the selective empowering of the Holy Spirit to worship. And the only legitimate way to assess any possible boundaries is to assess the empowering of the Holy Spirit. It seems to me that we do not have access to this data, at least with respect to worship.
We could, however, look for Holy Spirit empowerment in other more possibly verifiable contexts and postulate that Holy Spirit empowerment in these areas implies empowerment in the area of worship (though I believe a case for this could be made I will suffice to observe here that such a case is assumed to apply within the sociological bounds of Christianity.) This leads us to establishing criteria for assessing the empowerment of the Holy Spirit; in itself a tricky task. As with establishing any criteria we want to include everything that is pertinent without including anything that would give a false result.*
For the sake of argument I will propose that the fundamental work of the Holy Spirit is most simply to enact the "Thy kingdom come, thy will be done" of the Lord's prayer and that the multiple descriptions of the action of the Holy Spirit in scripture are examples of this fundamental work. From this I posit that an act that makes the earth more like heaven is empowered by the Holy Spirit. What follows is that if a Muslim acts in such a way that the earth becomes more like heaven then they are doing so by the empowerment of the Holy Spirit and that it is then reasonable to assume that they may very well, by the same empowerment, participate in true worship of God.
All we need then is a single example of this empowerment in more than one of the religions represented to falsify the distinctions upon which the interfaith discussion was based. We lose our beloved us/them beliefs. We are stuck with all just being people.
The obvious criticism of this line of reasoning is, "What about doctrine (a.k.a. believing the right stuff)?" To which I would respond, "What about doctrine?"
Doctrine is a network of logical propositions to which we may or may not give mental assent. If we set this mental assent to logical propositions as prior in importance to the work of the Holy Spirit then my reasoning falls down. However, buyer beware. With this we run into some at least equally severe problems. What doctrine is right doctrine? How right does it need to be? How much is enough? Who gets to make these determinations as to what is actually right and enough? What constitutes mental assent? Moreover, how could we possibly know with surety that we had the right answers to these questions; and, what difference would it really make other than enabling us to observe for ourselves who is in and who is out?
I do not see a really good reason for setting the priority this way. First, I don't see a good reason from the scriptural data since it appears that doctrine is derived from the Spirit rather than the other way around. And second, in the application, I just don't see anything of value gained and quite a bit of otherwise unfounded problems introduced.
This whole analysis leads to some very difficult implications. First, in a very important sense it places Christianity on a par with all other religions because it cuts the "in/out" pie on lines that show no intrinsic regard for religious commitments. From this a whole host of other Christianity-specific problems arise such as: why be Christian, why evangelize, what about the uniqueness of Christianity, isn't believing the truth important? These are all good questions to ask. So, let us ask them. If my reasoning holds,` then why be Christian, why evangelize, what about uniqueness and the importance of truth?
*This establishment of Holy Spirit empowerment criteria is something that I would be very interested in hearing from readers on.