Before following these steps check your GitHub pages website to make sure the problem is still there.
- From Godot export the project as HTML to a brand new empty local folder. (Make sure you export it as index.html since you intend to use the GitHub pages feature.)
- Delete every file from the GitHub repository and commit those changes.
- With the repository now empty, upload the newly exported files from your local folder to GitHub and commit that change. Note it takes some time for the changes to take effect on the GitHub servers ~5 minutes or so.
If the problem persists after following those steps there could be a bug in the export process for HTML, which you can notify the Godot developers of on GitHub.