[elcritch]

Partially true, but it's more complicated than this. Especially for Christianity.

Christianity did spread initially through the Roman empire despite broad persecutions by the state until Constantine legalized it. There's also evidence Christianity spread to Europe in the 2nd century before Constantine. It also spread to Ethiopia, Assyria, and even India, mostly by trade routes.

Christianity afterwards did spread with various European empires, but it also acted as a restraining hand as well. Some Christian missionaries went against the colonial states, in particular Protestant ones.