Users registered on the main site can't login on subsites on a multisite installation

bp-user-per-site.php

<?php
/*
Plugin Name: bPlus User per site
*/

// Url to redirect
define( 'BP_DEFAULT_URL', 'http://superpositif.com/interne/');

function is_valid_user_login( $user = null ) {
    // Current site
    $current_site_id = get_current_blog_id();

    if ( is_null( $user ) ) {
        $user = wp_get_current_user();
    }    

    if ( is_user_member_of_blog( $user->id, $current_site_id ) ) {
        return true;        
    }

    return false;
}

function my_check_user_blogs( $user_login, $user ) {
    if ( current_user_can( 'edit_posts' ) ) {
        return false;
    }

    // check if user is in the current site
    if ( ! is_valid_user_login( $user ) ) {
        wp_redirect( BP_DEFAULT_URL );
        exit();
    }

}

add_action('wp_login', 'my_check_user_blogs', 10, 2);


function my_set_default_blog_to_user( $user_id ) {
    // Subscribers are added to default blog
    if ( ! user_can( $user_id, 'edit_posts' ) ) {
        add_user_to_blog(1, $user_id, 'subscriber' );
    }
}

add_action( 'wpmu_new_user', 'my_set_default_blog_to_user' );

function my_check_user_access_for_site() {
    // check logged in users only
    if ( ! is_user_logged_in() ) {
        return false;
    }

    // dont perform check on normal users
    if ( current_user_can( 'edit_posts' ) ) {
        return false;
    }

    if ( ! is_valid_user_login() ) {
        wp_redirect( BP_DEFAULT_URL );
        exit();
    }
}

add_action( 'init', 'my_check_user_access_for_site' );