Keep Multiple Sites in Sync with WordPress GitHub Sync
Note: Using this feature, you are on your own. I may not be able to provide support for the configuration required to make this work.
Before you start, make sure both sites are in sync. Export the database from one and import it into the other, so the posts on both share post IDs. If the posts don't start with the same post IDs, things can go very bad.
In order to keep multiple sites in sync, use these two filters:
The sites can share branches, but they need to use their own commit message tags. This is how the site avoids resyncing commits it exported. If each site uses their own tag, then they'll only import commits that weren't from that site.
Finally, enable the webhook to deploy payloads to both sites.