I’ve run into the very problem you’re describing. Unfortunately, VMD exports state files as a single mesh. I found that it’s possible to separate them out using Blender’s Mesh->Separate->Selection command. Basically, go into Edit mode, unselect all the vertices, select the ones you want to separate, whether by Material or Select Linked, and then run the Mesh->Separate->Selection command. The selected vertices are then moved to a new object. It’s not exactly a streamlined workflow, but it does work for me most the time.
Another option is to save separate VMD state files, each with a separate representation, and then to import them separately. In some cases that might be more straightforward.
I hope this answer helps!