I tested now with using Fiddler Everywhere to inspect the traffic. As it turns out, as soon as I turn on the monitoring there, the requests start working again. I’m guessing because the requests are now routed through Fiddler. So I assume it has to be some sort of firewall change that causes this. I still don’t see why this would change between my UE 4.26 and 4.27 builds though, and why it’s not possible to get around by completely disabling the firewall.
Could be worth mentioning that this also happens on Amazon EC2 servers with the newer builds, but still works without issue with the 4.26 based builds.