Distribution through the Mac App Store will help, as users can see that Apple has tried your application and found nothing vile in it. [Added:] In addition, the sandbox of your application means that your application is limited by an explicit set of capabilities that can be tested by technically qualified users. You cannot do anything that is not listed, so this will be an easy way to prove that you are not sending anything over the Internet.
Another thing is to save all the data in files readable by the user. No binary disks, no Core Data storage, etc. (Whether the XML variants of any of these are considered readable by the user is more controversial, but for this purpose I think that at least the XML layer will be readable enough. About the main data.)
If the user can read all the raw data stored using applications that they trust (for example, TextEdit), and not just your usual idea of ββthe application in the application, then they can check themselves and, ultimately, trust that you do not store nothing that you would not like.
If interested potential users inform you that you are reporting your keystrokes to your own server via the Internet and suggest that you are not connected to Internet connections at all (even checking for updates), you can recommend Little Snitch should be installed in which displays a warning message at any time when any application is trying to connect to something. When they do not see such a warning about your application, they know that you are not calling home.
You can also provide a link to a technical profile on the product web page. Here's an Jesper article offering them , and here is one example of such a document, for one of its products .
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