The "Log in to GOG Galaxy" process is always using 5-10% CPU. Always. Why does this have to use so much CPU?

because it uses web browser, CEF - Chromium embeded framework . All apps with this hog will hog CPU, RAM, GPU. same goes for steam app. there's nothing you can do about it. maybe you can switch CPU utilization for GPU utilization if galaxy has settings to render pages with GPU instead of CPU (steam has it, not sure about galaxy).
anyway it still will hog CPU if you download and install games. It can be heavy load if you happen to have nice broadband. if it happens you can try to limit bandwidth for downloads.
Beside that I'm not sure if there's anything to tweak.