I can reproduce both the issues on my hosted site that’s on the latest Discourse code. Saving the “Auto update” option for one theme does not affect the “Auto update” option for other themes though. The issue could cause confusion, but it’s unlikely to cause the setting to be accidentally enabled or disabled for a theme.
This is only somewhat related to the issue in this topic, but maybe a “You have unsaved” changes modal should be displayed when navigating away from a theme with unsaved changes.