These issues happen when importing some of Rey’s demo sites. It happens because of how the header renders on Homepage & Shop vs. the rest of the site.
As you can see in these 2 examples, the Homepage’s header has a white color, is positioned over (absolute) the images and content, has a different logo (white) etc.
So in the Homepage’s case, the header’s settings are overwritten with custom options (different position, lighter logo, text color, or even a different header) in the page backend settings eg: https://d.pr/i/7JjdKD , because the header needs to overlap the content and stay transparent and visible.
Those header’s settings overrides the ones defined in Customizer > Header > General which are global and apply to the entire site.
The solution is either to unset the page’s header backend settings (or adjust them), or configure as you see fit to have a consistent design.
More on Header’s overlapping settings here .