With an additional plugin it's possible to render vertex colors of mesh with freestyle.

Download blender addon

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• 
• select the download file
• enable the addon
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To enable vertex color rendering go to Viewlayer > Linestyle → Freestyle color:

• vertex colors must be of type VERTEX
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• Freestyle geometry modifiers must not be active
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  • no active modifiers here
• for best reults Freestyle Chaining should be off