This issue usually happens when a demo has been imported on a WordPress site instance that already had (or has) content inside.
Basically the post IDs have been deferred and they don’t match anymore with the ones that were added from the import data files.
For example on a clean site, post IDs count would start from “0” and this ensures the Customizer’s data (such as the Header’s global section ID) will match the one that just has been imported. On a site that already had content though, the ID would start from a higher value, for example “200”.
Either access Customizer and simply hit the Publish button, or access Customizer > Header > General and make sure to pick a Header global section.