Gibbons hated christianity, so he blamed it on the Christians
However, a better explanation is the new presence of malaria in the swamps near Rome (Imported from North Africa) which does not kill adults, but kills babies and weakens people's ability to work. And then there were several very bad epidemics,including the bad one brought in from fighting the Persians. They think it was smallpox, but it could have been typhus or typhoid or even measles (which is fatal in new populations). The financial collapse, which was one of the causes of the French revolution, was also important to Rome. But when depopulation occurs due to disease, the tax base collapses (a problem more likely in socialist Europe than here).
The decadence of Rome led to promiscuity and the collapse of the native Romans. But then the the influx of new blood first from the other Italian states and later from other Roman provences allowed Rome to last a couple hundred more years.So multiculturalism was not the problem: Like St. Paul, these outsiders were proud to be Roman (just like my husband is proud to be an American and a vet despite the fact he was born outside the country). Rome fell because outsiders were taught to fight, and when they came into Rome they realized that Rome wouldn't fight for itself, but relied on mercenaries. Again, this shows more danger to Europe than to the US.
The History channel is supposed to have a program on Vespusius this week, the emperor who saved Rome. Might be interesting.