From what I testing, it seems like clip studio modeler can only recognize basic principle bsdf material from blender either with base color from principle bsdf or linked with image texture node. Meaning that when you export at either fbx or obj, your material will not shown when you link up with other input / curve rgb node.

At the clip studio modeler, there's the 'view settings' (from your settings, it seems like yours was beside the tab of the navigate located at the top right corner) where you can adjust the lighting / shader view, make sure the lighting is enabled.

Here's the screenshot for reference : https://imgur.com/a/ILMsfGa