Actually, I think Christianity is given far too much credit for destroying the Roman Empire. I think Brutus and the anti-Caesar conspirators deserve much more credit.
Rome's enduring strength was that it was that no single individual created the Empire or even the majority of it. The Roman system, the Republic, created the Empire. Great conquerors are all nice for stories and movies but they eventually die and successors do not do as well. Alexander's empire did not survive his death. All of Henry II's gains were eventually lost under his sons Richard and John. Henry V's conquest were lost after his death.
People forget that Caesar, before his death, was not that isolated a phenomena in Rome. There had been men before him who rose to dominate the state. His uncle Marius and latter Sulla did so in the previous generation. Yet, for all their power and glory, could not create a monarchy or a semi-monarchy. When they died, the Republic continued with power diffused over the elites of Rome. Even Caesar himself, after defeating Pompey, knew better than to try to be more than a servant of the Republic.
What made Caesar different was his assassination at the height f height of his popularity. Brutus and the other conspirators feared that Caesar would do what Caesar knew not to try, become a monarch. They couldn't chance it so they killed him. It turned into a self-fulfilling prophecy.
Octavian (aka Augustus) and Mark Antony used the emotional and political chaos after the assassination to wipe out the Republican opposition. Even men unassociated with the assassination, like Cicero, were murdered because they had stature enough to keep Augustus and Antony from scrapping the old system.
In the end, by killing Caesar, the conspirators had brought into being what they tried to stop. It happens often in history. On case, that is somewhat similar, is the assassination of of Abraham Lincoln. Booth made the final decision to kill Lincoln because he feared that Lincoln would not just end slaver but would also force black equality.
In reality, Lincoln may not have gone quite that far. Lincoln just proposed a constitutional amendment to end slavery before his death. Anything more might have been politically problematic even in the north. After the war, northern whites wanted it abolished because they felt it was wrong, the cause of all the bloodshed, or just to punish their former enemies. However, the majority of whites still could not see blacks as equal citizens. Even Lincoln himself was unsure how to go about it. His only stated commitment was to give citizenship to the black veterans. Beyond that, he just wasn't sure how far to go. This is not to condemn him. He was still a better man than most, but he was a politician as well as a product of his times. However, when Booth murdered Lincoln, a martyr was created. In the ensuing political and emotional chaos, radical Republicans pushed through constitutional amendments that guaranteed citizenship and the right to vote for blacks. Booth helped brought about what he wanted to stop.
Back to Rome. Augustus didn't totally dismantle Republic all at once. He and his successors just corrupted, ignored, and intimidated until they did as they pleased. Rome became a somewhat mirror image of the current British system. Britain has defacto republic with a dejure monarchy. Rome became a defacto monarchy with a dejure republic.
That sealed Rome's fate. It's highs and lows were tied to single individuals who came and went. There were great emperors: Augustus, Claudius, Trajan, Hadrian, Antonius Pious, and Marcus Aurelius. There were destructive emperors: Caligula, Nero, and Commidus. There were any in between.
Where a Republic spread power among many that balanced things out, a monarchy made Rome dependent on one person. On top of that, that one position of power became the object of every ambitious politician and general. In the Republic, no one person had too much power so there was no one office worth starting a civil war for. In the Imperial system, civil wars happened right and left as individuals bid for the ultimate office.
That destroyed Rome. The constant civil wars decimated the infrastructure, the armies, and leadership talent until it was too weak to resist the Germanic invasions.
The Christian movement was inconsequential in the face of that.