it looks like the wavefront (.obj) export is buggy in AC 21.
The objects don't keep their material definition.
I think the problem lies in that the material name in the .obj file can be different that the corresponding ones in the .mtl file.
Hope you can fix that soon GS.
I thought that Wavefront OBJ was more or less an archaic format?
Pending the bug fix ...
An easier workaround than saving back to AC 20 format and opening/exporting there, it seems to me, is to simply export a Collada DAE file from AC 21 and then use the excellent, fast and free Meshlab to open the DAE and then export it as OBJ from Meshlab. Meshlab can also export as PLY and other textured mesh formats as well.