How to enable Custom Fields that are disabled by theme?

Create a Child Theme, Plugin or Must Use plugin, and use add_post_type_support:

<?php
/* Plugin Name: Add CF to CPTs */

add_action( 'plugins_loaded', 'add_cpt_support_wpse_116891' );

function add_cpt_support_wpse_116891(){
    # See /wp-admin/edit.php?post_type=SLUG
    add_post_type_support( 'SLUG-POST-TYPE-1', array( 'custom-fields' ) );
    add_post_type_support( 'SLUG-POST-TYPE-2', array( 'custom-fields' ) );
    add_post_type_support( 'SLUG-POST-TYPE-3', array( 'custom-fields' ) );
}