It took more than a millenium before any serious challenge to that concept came forward, with the Reformation..." More churches. This is why some of our friends say, "I atten a Lutheran Church."
A church is a social institution that promulgates a particular religious doctrine. Similarly, --- and please do not read any kind of insult here, none intended --- a coroporation is a social institution that produced a good or a service. A family is social institution, endemic not to humans only, for procreation of species.
This is different from the religion iteslf, which is a system of values, rules, notions, etc. The distinction here is similar to that of "mathematics" and "Mathematics Department" at a university. The former is a body of knowledge, and the latter, of course, is a social insitution for the promulgation thereof.
Now, And one of the BIGGEST arguments, at least according to my own inquiries into the matter, seem to turn on the question of "what is PURE Islam?"
is a theological question. That is, it concerns with religion. Suppose there are three answers: A, B, and C. Those who follow these interpretations will form "A Church," "B Church," and "C Church," respectively. Each of them will believe that their is PURE Islam. This is what seems to have happened in Christianity, Judaism, and Muhammedism.
Which in the case of the Roman Catholic Church was a substantial number, the majority of Christendom.
And what's more, the nations that adhered to that particular Church included all the major world powers at one time or another, up until the Reformation.
Thus, when these people spoke of "the Church," and of "Christendom" and "Christianity," they meant the Roman Catholic Church.
Even now, the great majority of non-Roman Catholic Christian sects--not including my own, as it happens--are descended from Roman Catholicism.
In effect, for probably five-sixths of the world's Christians, the Roman Catholic Church is "the mother Church" and synonymous with Christianity itself.
Again, note: I have no personal agenda in this regard; I am a "Mormon" and we claim no relationship or tie to Roman Catholicism whatsoever, and many of our doctrines are very foreign to the Roman Catholic tradition.
I'm speaking in the Historical sense, while you are preoccupied with abstract philosophical concepts (no insult intended, that's just an observation).
And in Human Events, the REALITY of history is more important than the tenets of philosophy.
Back to my original point: This is why people here and elsewhere tend to blame ALL ISLAM for what a relatively minor offshoot of Islam is doing in "fighting jihad."
It would be like targeting "Mormons" for reprisal in some obscure part of the world because, four hundred years previously, a Roman Catholic nation like Spain had subjugated the people there. Those who don't understand the distinctions, and the subtleties of philosophy, would be apt to make such a a connection when there is none.