People who say it was the chief cause are wrong, and people who say it had nothing to do with it are also probably wrong. Some of the people you pinged will give more examples and details, but I'll simply relay what I frustratingly tell people who take the "it was the primary cause."

If christinization was such a powerful force that led Rome to collapse, then why did half of the Empire survive for another 1000 years despite being a basic authoritative theocracy? The John Haldon Book Warfare State and Society in the Byzantine World (This isn't the actual title, but it's what I have at the top of my note sheet for some reason, I'll get the actual title once I'm home), for example, goes into depth in the first chapter how the Byzantines remained martial in nature despite being heavily Christian. Warrior saints were common, the fighting of the infidel was often focused on especially with the later Macedonians, and the church recognized that the state had to defend itself because the Empire was God's kingdom on Earth. Because of this cooption of christian thought for martial reasons being done so well in Byzantium, I'm inclined to argue that the West's collapse was much much much much more due to the litany of other reasons that the West collapsed such as demographic decline.