I imported everything, and the problem persisted. I created key frames, and the probnlem persisted. I got really angry... and got rid of it :P

The clue was that Blender unexpectedly flipped some normals of some objects inwards! When I inspected my meshes, I realized I had to recalculate them out. After that, it worked again. It`s extremely strange since I imported this model for C4D a couple of months ago and already made a project with it and had no trouble. Blender really lives its own life...

"Presume nothing", wasn`t it its ad slogan a couple of years ago? :P