Hello.
Our company also encounters such problem.
All browsers can successfully display company web-site (bfshina.com.ua), but after Opera VPN enabled - it display error with Nginx (we are using Apache) http://bfshina.com.ua/operavpn_fails_on_access.png. Web-server log shows, that query was successfully accepted and data send back to client agent: http://bfshina.com.ua/other_sites_access_log_with_opera_vpn_IP_connect_tries.png.
Thanks for help.