On the other hand, quite a number of them are quite clear on who (according to them) is not part of the True Church.
And even if you suggest otherwise -- is there any other way to explain the many, many schisms within protestantism without some reference to specific beliefs about "true" vs. "false" churches? Why would a schism occur, if not because of some perception that my take on the true church is correct, whereas yours is not?
Are such divisions "of God?" I don't think so. Rather, I think they're manifestations of human pridefulness. Even when one is right, and believes all the right things, there are still wrong and sinful ways of trying to express it.
Heck, even Moses fell into that trap, and in consequence was not allowed into the promised land.
I've learned the hard way about the need for humility when dealing with disagreements over church matters. That includes debate on religious topics.
If you study carefully the various ‘schisms’ in Christianity, most are matters of governance or minor doctrines not major ones.
I think they can be ‘of God’. God gives us different ways of worshiping Him, differences in worship styles, and focii, but MOST Christian churches agree on the major points of doctrine, the important things like Salvation by Grace not works, Christ’s payment for sins on the Cross, the Virgin Birth, Sinless life of Christ. Most other things are relatively minor (like governance).
And to repeat, I do NOT like church fights over minor doctrinal differences, I think those can be about pride and cause division in the Body of Christ.
However, I also do not tolerate groups that don’t agree on the biggies (like those above) such as Mormons to CLAIM to be Christians while believing in a VERY different Christ. That is where I draw the line.