What are best practices for settings (UI) like this? I am looking to find out more about good practices, good UI/UX for this component for removing, adding items to different profiles (profile 1 has different added items than profile 2). Are there any good examples of UI/UX design for this?
How many elements are you dealing with? What do you mean by 'Profiles'?
Knowing more about your current context will help with deciding what will work best. Elaborate or show more of your problem and I'll update as I can to be more helpful to your specific situation.
The example you provided is using a list builder to customize a toolbar.
The list builder can be a helpful element. There are some alternatives. Some mac os software instead allows you to directly drag, drop and reposition element on a toolbar directly:
The advantage here is you don't have a disconnect between the current elements and their position, and what you can add and reposition: it's right in front of you.