I actually update this a week ago, but apparently I forgot to create a blog post.
Several week ago, My client reported that he cannot reset the password on his sandbox private site. I investigate, and found that WooCommerce actually change the lost password URL to WooCommerce “My Account” page. And because this page is set to private by f(x) Private Site, user cannot reset their password.
So this update (v.1.2.0) address this issue. And now WooCommerce my account page is white-listed and still accessible when you set your site to private using this plugin.
I also add better BuddyPress Compatibility, Even though it’s working well with this new method (as suggested by Paul Gibbs, BuddyPress Lead Developer) This method will be more future proof.