Security

Would there be any production issue if a backup was taken of a publisher and subscriber node of clearpass?  I have not performed a backup myself yet and did not know if this would hinder any performance.

My understanding would be going to Administration > Server Manager > Server Configuration > Select server > Select backup

You can leverage the automated backup files stored under Administration » Server Manager » Local Shared Folders. You can configure Auto backup configuration options under Cluster-Wide Parameters » Database settings. 

Why do you want to take a backup of the subscriber node separately? 

Publisher backup will have all the data of subscribers, configuration of subscribers is in sync with publisher.

Is there any specific reason looking for subscriber backup you can take only publisher backup. Default  clearpass will take backup which is stored under Administration » Server Manager » Local Shared Folders > Auto backup , if you want manual backup you can execute from Administration » Server Manager » Server Configuration.

There wont be any production issue, if we take manual backup.