Why Facebook Image Gallery displays only public Facebook albums?
Due to limitations on the Facebook Token that Facebook Image Gallery uses to gather the album images, the albums need to be completely public to be displayed in your store.
If you check our examples, as for instance:
They can be viewed with a browser where you are not logged in on Facebook.
In other words, the album has to be fully available for all people without the need of having a Facebook user, as it will be displayed publicly on your page.