For sites with stringent security policies, there should be an option when generating a support bundle (or perhaps just a global setting applicable also to auto-generated bundles) that would search for mentions in all files of labels created by the customer which might reflect proprietary processes: job, folder, view, slave, and template names, slave labels, etc.
The plugin would gather a list of all such labels, create randomized tokens, and produce a mapping so that a job AppBuild becomes Job_ayrzw. For labels with spaces or other special characters, which could have triggered bugs, the mapping should follow, so App ? Build should become Job_ayrzw ? X, and the mapping should also include encoded variants such as App%20%E2%86%92%20Build to Job_ayrzw%20%E2%86%92%20X and App%20%e2%86%92%20Build to Job_ayrzw%20%e2%86%92%20X.
Then these substitutions would be applied to all files included in the support bundle, particularly log files and thread dumps.
It is impossible to guarantee that customer text does not appear in some unusual context, e.g. an exception quoting a syntactically incorrect Groovy script, but these substitutions would sanitize the great majority of what the support bundle produces, and make it feasible for the customer to do a final inspection without needing to do much or any manual editing.