Due to climate change and the Hunnic migration, among other factors. But only the old Western part of the Empire fell. The by this point far richer Eastern provinces remained quite powerful for centuries, at times even reclaiming much of the Western empire at times. And the Eastern Roman Empire remained a bulwark of Christianity. The schism between East and West was political as well, and had to do with the Western Pope in Rome attempting to claim political legitimacy from the Eastern Emperors.
Regardless, the Roman Empire survived, in its rich Eastern holdings, until 1453 when it was conquered by another mighty Empire which drew its legitimacy from monotheism- the Ottoman Empire.
Meanwhile, empires from the Carolingian to the west to the Russians in the north and their descendants traced their legitimacy back to the Western and Eastern Roman Empires until their fall following the first World War.
It doesn’t matter how legitimate these claims may or may not be. What matters is that the Roman Empire, with its strong ties to monotheistic Christianity, remained an important political tool right up until heredity rule was supplanted by modern ideologies in the Western world. Arguing that Rome’s legacy ended when its old capitol was sacked, despite the prosperity the Eastern empire would continue to enjoy for centuries, and the enormous influence it had on the west, is just ridiculous.
Europe was Christianized because Rome was Christian, and converting - even if only on paper - was a powerful tool for “barbarian” kings who sought to trace secure their legitimacy by attaching it to Rome’s.
Odoacer - the barbarian king who took Rome in 476 - was a Christian. While the Eastern Romans dubbed him a conquering king, Odoacer used the title of Patrician. He took power with the cooperation of the senate, and he presented himself as a client of Zeno, Emperor of the East. So even if you buy the argument that Odoacer’s rise marks the end of Rome in the West, its influence is still clearly felt, and the Kingdom of Italy is more of a successor state.
The next King, Theodoric of the Ostrogoths (also a Christian mind you), was raised in Eastern Rome after being taken captive in his childhood, and invaded Italy at Zeno’s request. He was another ‘Patrician’ for Zeno, and he conquered vast expanses of formerly Roman land.
He was succeeded by Athalaric, who minted coins with Justinian’s image on them:
He was also a child, so his mother acted as regent. By the time he was 18, he drank himself to death, so his mom needed a new co-ruler. She chose Theodahad, a relative, who soon was accused of stealing land leading to instability in the kingdom. Which was the pretext that Emperor Justinian needed to send in Belisarius, who reconquered much of the lost territories.
That’s a Roman Rome in 565, another 100 years after your 150 year figure; and in all that time, it always had a Christian rule.
The Romans would lose control of Italy once more by the late 570s, this time permanently, to the (Christian) Lombards. They also take some territory in Southern Italy, but Rome is still under Imperial control as is Sicily and a number of other regions in Italy proper; many won’t be conquered until the Norman invasion in the 900s-early 1000s. Guess what religion the Normans were?
Rome’s legacy, and the use of monotheism for political control, did not end 150 years after Rome adopted Christianity. Arguing that it did is simply preposterous.