Obj export : All normals are flipped

No such problem with Fbx export :no:

boots1Test.blend (478 KB)

Your object has negative scale - so, in fact, the normals are inverted:

Select the object and hit Ctrl-A > Scale.

Outside of animation it’s hardly ever a good idea to work with unapplied scaling - and even less so with negative scale values.

@IkariShinji thanks a lot, you made my day