Hi @Hielke Rijpstra so your issue is the customer see or don't see watchers? My past experience shows they shouldn't be able to view watchers or votes as they are part of Jira Software license, visible to in-org users, while customers can see "recipients" as part of Jira Service Desk license.
@Hielke Rijpstra the Share With is not the same as Jira Watchers.
Jira Service Desk allows added what was referred to in the past as Participants and it allows agents and customer to add customers there.
Customers can't add "watchers" from your internal org.
Why would you want to prevent customers to add their fellow customers to a request?
@Hielke Rijpstra you might want to try this option to disable a module in your add-ons/app page: https://community.atlassian.com/t5/Jira-Service-Desk-questions/How-to-remove-quot-Share-with-Customer-quot-button-from-a/qaq-p/738897
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