HDMI has an Ethernet channel
https://en.wikipedia.org/wiki/HDMI#HEC
Any chance the TV can phone home via that? One would have to make sure the HDMI cable physically doesn't have the Ethernet pairs, or set the trusted box to filter the traffic.
The HDMI standard defines an Ethernet channel as an optional feature. Approximately zero consumer products have ever implemented it. There's no need to worry about an unsuspecting consumer having supporting devices at both ends of the cable.
And the channel they allocated for it was reallocated with different encoding for eARC.
I don’t know of any consumer laptops or tv boxes like shield/Apple TV that implement that so that. It’s basically a non-issue unless it’s implemented on the HDMI devices.
If you use something you can control, like a Linux box, this isn't an issue. Even if the device did get added, and then udev or network manager auto configured, a firewall script should protect you.