Twine allows you to edit what information users can view on each other's profiles. Public information is available for everybody to view, whilst private is only viewable by admins and the user themselves. This is shown on users' profiles as in the image below.
As an admin, you can configure what information is shown which section. To do this, go to Settings > User Data > Custom Fields.
Here you can configure if custom data fields are public or private by using the dropdown menus. When you're happy, press Update Settings.