Hi Eric,
From your post, my understanding is the anonymous users cannot see the App Parts you inserted when visit your public-facing website.
I tried to insert App Parts to reproduce the situation. Based on my test, I found that there would be a “Recent draft not published” prompt after inserting a new App Part. If I did not click “Publish this draft”, the changes were not able to be shown by visitors, who are anonymous users.
If it is not the root cause, I will appreciate it if you can provide the details about your situation, for example, the following collections.
1. Which plan you are using, Home Preview, Small Business Preview or Enterprise Preview?
2. The detailed steps that you added the apps to your public-facing website, and which app did you add?
3. Did all apps you added cannot be shown or just special one?
Thanks,
Maggie Li