I started getting blocked, too, on Jun 2. My ISP is Verizon FIOS, so will be a long time before they get IPv6. I've been running a HE tunnel for years and it has worked perfectly. Have a CISCO 1921 router but been a long time since I waded through the IOS to set up the router. If anyone figures out how to tell CISCO IOS to only provide IPv4 on the interface used by the Apple TV ver 4 I can connect the two Apple TV's to two ethernet interfaces on the CISCO 1921 and get Netflix back without having to drop the IPv6 Tunnel.
I tried setting DNS on the Apple TV ver 4 to Google's DNS server, 22.214.171.124 but for some reason the Apple TV still defaults to IPv6 and Netflix reports back:
Streaming Error You seem to be using an unblocker or proxy. Please turn off any of these services and try again. For more help, visit netflix.com/proxy.