Ok, I found out that this theme is not compatible with Cloudflare service.
I am disabling the Cloudflare, and it works fine. I have few other sites with a different theme that has no problem loading on IE11 with Cloudflare/railgun activated.
Kindly look into it when you got a chance. Thanks!
I assume the sole fact that CloudFlare is used can’t be the reason for failure. It’s probably a problem with CloudFlare configuration (old cache, or smth else), or a combination of CloudFlare with something else (like a third-party caching/minimization plugin, etc.)