Microthemer works on any page that is generated by WordPress (where any JS and CSS resources a plugin uses are loaded). Maybe your checkout page is special somehow, but that’s unusual. If you can select and edit some elements, the issue is likely specific to the element you are trying to change the color of. Perhaps you need to select a parent or child element. Why element have you tried to change exactly?
Ah, so if clicking doesn’t select anything there might be some scripts running on that page that are blocking Microthemer from selecting elements. If you don’t mind sending temporary access details for the affected site via our secure contact form I would be happy to troubleshoot this for you.