Updating themes customized by users

Short answer: yes.

Long answer:

The Customize API uses one of two methods for storing customizations: the Settings API or the Theme Mods API (the latter being the default method). Thus, all changes are saved to the database, either as a Theme-defined option, or via theme_mods_{themeslug}.

When the Theme is updated, the Theme files in /wp-content/themes/{themeslug} are deleted and replaced, but the database entries in wp_options remain untouched.

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