If you want a user to only edit specific fields for their organisation you can create a profile and add the organisation fields you want to give them access to. From the CiviCRM profiles page:
CiviCRM Profile(s) allow you to aggregate groups of fields and include
them in your site as input forms, contact display pages, and search
and listings features. They ...
Welcome to Stack Exchnage Hans-Christian.
The latest version of CiviCRM contains changes regarding the display of custom tabs in the contact view that also affect CiviSEPA. You should be able to fix the described issue by upgrading to the latest CiviSEPA version (1.5): https://github.com/Project60/org.project60.sepa/releases
We have used contact layout editor extension to show only necessary fields on view contact section. Using contact layout editor you can customize the view contact page. You can include profiles with limited fields and hide or remove the edit option via css or JS.
Or other option is write extension to redirect Org contact to /civicrm/contact/dashboard?cid=123&...