Unfortunately, you can't export the objects to different DWG layers based on the object material in Revit.
When exporting to DWG, you can set Layer Modifiers to create a rule how the objects of the same category will be exported to different dwg layers. But the rule available is limited currently.
For example, you can export the pipes, fittings, etc to different layers based on the system type, you can also export the walls to different layers based on the structural usage, function, etc. But it doesn't provide the material parameter as the rule.
You can check the post below to get detail information about layer rule setting when exporting to dwg.
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