Filter the MultilingualPess admin metabox to allow for connecting translations to other post types on remote site.

multilingualpress-cross-post-type.php

<?php
/**
 * Filter the post search arguments allow for cross-post-type connections.
 *
 * @param array $args the WP_Query arguments used.
 * @return array
 */
function remote_post_search_arguments( $args ) {

	$translated_post_types = array( 'post', 'page', 'product' );

	if ( isset( $args['post_type'] )
		&& is_string( $args['post_type'] )
		&& in_array( $args['post_type'], $translated_post_types, true ) ) {

			$args['post_type'] = $translated_post_types;
	}

	return $args;
}

add_filter( 'multilingualpress.remote_post_search_arguments', 'jdn_remote_post_search_arguments', 100, 1 );