First off, you’ll obviously need to be using the same parent theme for all sites. You then set up each sub-site with a child-theme for that parent theme.
To use the same stylesheet on multiple sites, add the following code to the functions.php file of each sub-site:
function import_shared_style_sheet() {
wp_enqueue_style( 'shared-style-sheet', content_url( '/themes/SOURCE-THEME/style.css') );
}
add_action( 'wp_enqueue_scripts', 'import_shared_style_sheet' );
SOURCE-THEME needs to be replaced with the folder name of the theme you are sharing the master styles.css file from.
Keep in mind that the styles.css file of the child-theme of each sub-site will still load. So be sure to remove all css from below the theme data at the top of the file. For example, you should only have something like the following (it will differ, based on whatever child-theme you are using). In this example, the parent theme (for all the sites) is twentytwenty, so the shared styles.css file is in a twentytwenty child theme.
/*
Theme Name: Sub-site Theme (child theme)
Theme URI:
Template: twentytwenty
Author:
Description: Child theme of Twenty Twenty. Shares style.css of XXX child theme.
Version: 1.01
Updated: 2021-02-01 01:14:52
*/
Note, that if you end up with some styles you need to apply only to a specific sub-site, you can still add those styles to the styles.css file of that sub-site’s child-theme styles.css file.