ai91

Update: ended up with introducing own solution.
The workaround with native php session works, but not really nice: the Social Login plugin successfully logs in, but redirect url always points to main domain, without any subdomains (used WORDPRESS_SOCIAL_LOGIN_HYBRIDAUTH_ENDPOINT_URL constant, which is always on main domain, as result on successful login browser was redirected to same domain).

To solve the issue, replaced WORDPRESS_SOCIAL_LOGIN_PLUGIN_URL and WORDPRESS_SOCIAL_LOGIN_HYBRIDAUTH_ENDPOINT_URL constants with own functions, which build urls dynamically, based on current HOST. :

homeurls.php
===========================

<?php
function wsl_plugin_url()
{
	$protocol = ((!empty($_SERVER['HTTPS']) && $_SERVER['HTTPS'] != 'off') || $_SERVER['SERVER_PORT'] == 443) ? 
		"https://" : "http://";
	$domainName = $_SERVER['HTTP_HOST'];
	
	$plugin_url = plugin_dir_url( __FILE__ );
	$plugin_path = parse_url($plugin_url, PHP_URL_PATH);
	return $protocol.$domainName.$plugin_path;
}

function wsl_hybridauth_url()
{
	$hybridauth_url = wsl_plugin_url() . 'hybridauth/';
	return $hybridauth_url;
}

================================

then replaced all constants usages with

require_once WORDPRESS_SOCIAL_LOGIN_ABS_PATH . "homeurls.php";
... wsl_hybridauth_url() ... instead of  WORDPRESS_SOCIAL_LOGIN_HYBRIDAUTH_ENDPOINT_URL 
... wsl_plugin_url() ... instead of  WORDPRESS_SOCIAL_LOGIN_PLUGIN_URL 

Now I don’t need the native session support. And user becomes logged in domain he uses.