Click on export, and choose “custom” export method.
Lets say you want to export first 20 tables only.
Open chrome or browser console [ctrl+shift+j], enter the following:
$("input[name='table_data[]']").slice(0,20).click();
For next 20, use 20,50 as arguments in slice function used above.
The customizer data is stored in table wp_options under option_name theme_mods_THEME-NAME
you can view all such settings via the following query:
SELECT * FROM `wp_options` WHERE `option_name` LIKE "theme_mods_%"
In some cases, you just want to use parent theme’s settings in newly added child theme. If that is your case too, use the following queries to utilize and close those settings for your child theme also.
update `wp_options` set `option_name`="theme_mods_YOURCHILDTHEME_backup" where `option_name`="theme_mods_YOURCHILDTHEME";
insert into `wp_options` (`option_name`,`option_value`,`autoload`) select "theme_mods_YOURCHILDTHEME",`option_value`,"yes" from `wp_options` where `option_name`="theme_mods_PARENTTHEME";
The following one is a bit risky one. If you understand what is going on here, go ahead.
delete from `wp_options` where `option_name`="theme_mods_YOURCHILDTHEME";
insert into `wp_options` (`option_name`,`option_value`,`autoload`) select "theme_mods_YOURCHILDTHEME",`option_value`,"yes" from `wp_options` where `option_name`="theme_mods_PARENTTHEME";