There is an issue with “Custom object” texture mapping and edge softening - in short words it messes up texture mapping.
As soon as you enter the UV Editor (without changing anything inside) and hit apply, mapping changes from Surface Mapping to Custom object, and from there, if your object has edge softening applied, after exporting to other programs, UV layout is messed up. The same goes for previously Unwrapped objects.
I don’t know if it’s true for all objects (probably not always) but this simple (valid) polysurface was a showstopper for me.
Can you reproduce this bug and fix it, please? I just had to stop with my work because of that.
As my testing software, I used Blender and UE4, geometries created in Rhino 7.3.21012.11001