Disable Updates in WordPress

Add the following to wp-config.php:

// Disable core updates.
define( 'WP_AUTO_UPDATE_CORE', false );

Add the following to the theme's functions.php or a custom plugin:

// Disable plugin updates.
add_filter( 'auto_update_plugin', '__return_false' );
// Disable theme updates.
add_filter( 'auto_update_theme', '__return_false' );

There are many more things you can do to really hinder those pesky updates. Check out the source code for "Disable Updates" plugin: https://plugins.trac.wordpress.org/browser/disable-wordpress-updates/trunk/disable-updates.php.