There are two diffent type's of HDMI extenders.
The first type is simply using cat5/6 as a cable medium to transfer the data, this in no way has a routable IP address.
Then there are HDMI over lan adapaters that give the display a routable IP address.
There is no reason why these can not be on a vlan or be accissable across VLANs if you configure your firewall rule appropriately