That article sums up the cooling of Tolkien and Lewis's friendship quite well, Ady. Though Lewis's anti-Papacy may have been more of an affectation than based on any deep-seated theological conviction. I think Lewis's attempts to insinuate Joy Gresham into the Inkling meetings, and his blatant proselytising in a culture where religion was seen as strictly private, did the most to damage their relationship. Though as far as I know Tolkien never totally disowned Lewis.
An interesting point about both Lewis and Tolkien, is that their views on Christianity were based not so much on theological grounds, but Mythological grounds. Here is part of an essay I wrote based on my research into this topic:
For answers to this mystery we must turn to Tolkien. Tolkien was similarly enamoured by Medievalism and believed one could not merely analyze with Reason the Old Poets and Mythology. He thought one could only truly appreciate such things on their deepest imaginal level. He discovered the Anglo-Saxon poet Cynewulf in his youth and in the poem Crist came across these lines:
Eala Earendel engla behrtast
Ofer middangeard monnum sended.
(Hail Earendel, brightest of the angels,
Sent to men upon Middle Earth.)
Earendel could be crudely translated “shining ray”—however Tolkien thought that this bright ray was more accurately Venus (pagan) and also applied in this case to John the Baptist (Christian). Earendel would eventually become Earendil, the Mariner who carried the Morning Star across the sky in Tolkien’s Silmarillion.
One night in September 1931 Lewis, Tolkien, and Henry Victor Dyson dined together at Magdelen. Wilson notes that Owen Barfield had already broken down the arbitrary distinction between “myth” and “fact” (much like Joseph Campbell would later popularize). He also pointed out that early users of language didn’t distinguish between the metaphorical and literal meanings of words. When the wind blew it wasn’t “like” someone breathing, it was literally the breath of a divinity.
Tolkien’s approach was similar. As Wilson describes it, Tolkien’s Elves are animist, pagan. It is humankind in Tolkien’s world who are to move beyond this. For the Elves being immortal will never leave the material world and do not know what will happen to men after they die. The Elves therefore are the embodiment of language users for whom the wind/breath/spirit distinction is apparently meaningless.
Apparently when Tolkien dialogued with Lewis that September night, he was arguing for an “Elven” approach to the Gospel story. Lewis had no problem being moved by the stories from other ancient mythologies, but he had trouble seeing the relevance of Christ to his own life. It would seem that Tolkien explained that Lewis had only been looking at the story with an empiricists viewpoint and that he should simply understand the story of Christ as a True Myth (I suppose as opposed to the other myths? 
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But Tolkien’s argument would be even more nuanced. Tolkien argued that the Doctrines which are extracted from the myth are less true than the actual myth itself. Lewis would argue that was tantamount to “breathing a lie through silver.” This riposte led Tolkien to reply in writing with the verse Mythopoeia. In essence Myth was the opposite of a “lie breathed through silver;” man’s capacity to mythologize was a remnant of his ability to see into the life of things (animism). All creation was “myth-woven and Elf-patterned.”
The fascinating upshot then seems that Tolkien used a Pagan argument for Christianity which largely is responsible for Lewis finally accepting Christianity, yet Lewis would then go on to Rationalize Christianity through apologetics whilst giving freer reign to his Pagan unconscious through prose. To me this suggests to me, that no matter the outer trappings of their particular denominations, they both had a view of Christianity that put them outside the mainstream of Orthodoxy and closer to the views of someone like Joseph Campbell or Mircae Eliade and even Alan Watts. I think had they been born a generation later their natures would have put them both in a more universalist camp.
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. Yeah, I alerted NWeb as soon as I saw Ady's post. You must have got the NWeb news alert.