The Groovy Postbuild plugin doesn't appear to adhere to the Jenkins.RUN_SCRIPTS permission at all. I'm generating jobs using the Job DSL Plugin and have given the RUN_SCRIPTS permission to the anonymous user.
When I generate scripts this plugin still requires the script approval.
Authentication is enabled but anonymous is given RunScripts permission. I would assume anybody would be able to create scripts (including the Job DSL plugin generated jobs).