I add one function wp_set_current_user for setting up current user.
add_action( 'wp_ajax_facebook_login', 'facebook_ajax_login_or_register' );
add_action( 'wp_ajax_nopriv_facebook_login', 'facebook_ajax_login_or_register' );
function facebook_ajax_login_or_register(){
$uid = sanitize_text_field( $_POST['uid'] );
$args = array(
'meta_key' => 'fbuid',
'meta_value' => $uid,
'meta_compare' => '=',
);
$fb_user = get_users($args);
$current_user_id = $fb_user[0];
wp_set_current_user($current_user_id);//Set current user
wp_set_auth_cookie( $current_user_id, true );
$response[success] = true;
echo json_encode($response);
die();
}
I’m not tested this so let me know if still you facing same issue.