This appears to be an issue with all asset types, not specific to materials. Data Tables, Level Sequences, etc.
Image shows the "No" cursor that shows up when attempting the drag/drop. This should ideally show a green "Yes" cursor and highlight the field like the Details Panel does.
1. Create a Static Mesh variable.
2. Create a "Set Material" node.
3. Find a Material in the Content Browser
4. Drag and drop the Material from the Content Browser to the "New Material" slot in the Set Material node.
5. While hovering you will be presented with a red circle with a cross indicating the drop target is not valid. If you release the drag/drop it will assign the material as expected.
There's no existing public thread on this issue, so head over toAnswerHub just mention UE-68484 in the post.