BuddyPress.org

Great, glad that fixed it! You can see the list of WP actions here: https://codex.wordpress.org/Plugin_API/Action_Reference.

To limit this redirect just to the home page update it to something like this:

add_action( 'template_redirect', 'redirect_visitors' );
function redirect_visitors() {
    if ( !is_user_logged_in() && is_front_page() ) {
	wp_redirect( site_url() . '/my-site-registration' );
        exit;
   }
}