I ran into a frustrating issue where my KVM VMs would lose network connectivity if I installed docker on my Arch Linux system. After some digging I finally discovered the cause (thanks to anteru.net)

It turns out, docker adds a bunch of iptables rules by default which prevent communication. These will interfere with an already existing bridge, and suddenly your VMs will report no network.

There are two ways to fix this. I went with the route of telling docker to NOT mess with iptables on startup. Less secure, but my system is not directly connected to the internet. I created /etc/docker/daemon.json and added this to it:

{
    "iptables" : false
}

Then restarted my machine. This did the trick!