I love the idea of the plugin but dislike the name. It is a bit misleading. This will not work with all themes that use the customizer. It will probably only work with a handful of plugins because most plugins wouldn't save their options as theme mods. It would've been more accurately named Theme Mods Import/Export.

See, the Customizer is not an API for storing/retrieving options, so there's really nothing to import or export. It's an API for displaying a settings screen. Plugins and themes can store settings in 1 of 4 ways: theme mods, single options, array of options, or something custom. A theme can even use a combination of those methods, depending on the circumstances. The only method that is standardized for figuring out settings is theme mods. With that method, you can grab the correct option from the database.