Skeletal mesh importing is broken, doesn't import face normals

Very same file, same settings, same material.
The only difference is the “Skeletal Mesh” checkbox.

This is what I get with skeletal mesh import disabled:

This is what I get with skeletal mesh import enabled:

What the WTF is going on?
I’ve tried every possible piece of software and export option, nothing makes any difference.
UE4 just ignores any and all face normals when importing a skeletal mesh.
Yet all the normals are in there and they are clearly fine, it’s the very same file.

Even tried importing the mesh to mixamo and exporting it from there.
And not only this mesh, but also other meshes.
Makes no difference.

Even exporting from the UE and then reimporting it back gives the same broken result.

How the ■■■■ did this happen?

It appears I can import this model just fine in a new blank project.
But when migrating to the main project, it breaks to this.
What the ■■■■ is going on?
How can UE be so broken?
What am I supposed to do?