"Aggressively secular societies". They were not that. In all cases the leader became "God". And the people, to a horrible degree, were true believers.
There are some interresting paralels between marxism-leninism (in its muliple incarnations) and eschatological cults.
(Marx was raised in the Prussian Lutheran Church.)
"The forces of history" is God.
Marx is its Prophet.
Revolution is the End Time struggle.
Lenin/Stalin/Mao/Pol Pot etc. is the Second Coming.
Communism is Heaven on Earth.
Marxism likes to dress itself in sciency gobbeldygook, but Marx, or anyone following in his footsteps, have never been able to actually proof their basic premisses.
Like pretty much all ideologies it's faith based.
ETA: This probably explains why regimes based on such ideologies tend to clamp down on organised religions.
Nobody likes competition.
I don't see how it could be exempt from burden of proof, even if you are just making the claim to yourself.
And my point is you can't apply burden of proof in the first place, since there is no possible way to prove it. It's not an exemption: it's a completely different ball game.
Why?
Why would you want to exclude the believe in the supernatural from rational inquiry?
Without it it will never become knowledge. Something much better than mere believe.