This is a short post as I need urgent assistance with this issue, It has been a regular occurance for me recently and I need to find a way to overcome this.
Try exporting this model as an .obj file instead of fbx, fbx file contains texture which overrides part color, if you want your previous models to use color instead of black texture check in their properties if they have any textureID, if yes then delete this ID, that should probably do the work.
If you don’t want a texture for the mesh, one of your only remaining options is to separate the mesh into whatever respective colour/material you want the end asset to have. So join together all wood of one particular colour, all wood of another colour, all stone of one colour, etc, and export those joined objects into one .obj each.
This method can cut down an asset made of 30+ objects into three or four objects, which is much easier to import. Just check the Selection Only box while exporting the .obj so that it’ll only export the object you have selected.