Recently, Atlassian added support for public links to Confluence pages, so you could share internal content with a broad audience. Readers don’t even need an Atlassian account to access it. This works nicely for basic pages.
However, if a page published this way uses the Include Page Macro, readers will just see a note in its place explaining that they’re not allowed to see everything. This does not change at all if the included page is made available publicly, too.
Atlassian documentation has this to say about content visibility:
Visitors to a public page will see a safe, view-only version of the page that was shared which hides any content outside of the shared page (page tree, macros, etc.) and locks most Confluence functionality.
Therefore, I believe this is working as designed. Atlassian does allow some macros, though; as of writing:
Is there any workaround to have some content be reused on public Confluence pages (other than lobbying Atlassian to change the handling of the Include Page macro)?