>>meindn+fc
Not sure if I would lump all those up together, these examples are overly broad and have little in common. There's more than a thousand years and basically no causal link between Roman persecution of early Christians and Crusades, let alone European imperialism, especially if you take Ethiopian, Greek, Georgian, and Armenian Christians into account. Same for Russians and Mongols, there's a pretty large gap with a ton of events in between, and Mongol Empire was humongous to begin with, it wasn't about Rus' in particular. And communists that became ruthless oppressors were already radicalized during the persecution, it was literally the radical wing of a militant faction of a huge umbrella party that included people that would have felt right at home in modern EU (e.g. Kollontai and her early activism).
The better explanation is simple and banal - power concentration makes people abuse it.