OK, I do not have much to add, other than confirming that Cloth/Hair are not transparent to FBX export.
You have 2 choices:
One, is to export whole figure as alembic and redo ALL materials in Blender.
Two, hybrid export as I have shown in the link (here it is again:
https://forum.reallusion.com/FindPost456897.aspx )
In this case you export animated model to FBX and then separately export Physics enabled cloth/hair as alembic and import both into Blender.
Then delete/hide cloth/hair arrived to blender with FBX.
The advantage of hybrid method, is less hassle with materials. Here you have materials for body mesh and non-physics cloth. You only need to tweak them.
But for soft cloth/hair, you'd still need to rebuild materials from scratch.
I do not see any other alternative to those 2 methods... except maybe to animate hair and other soft cloth directly with Blender physics (whole other story).