Docker adds iptables rules that break a lot of things including MASQUERADE or anything that needs the FORWARD table. If NAT is not working after Docker installation, it is probably because it set the iptables FORWARD policy to DROP. This may also make you think that your br0 or bridge is not working, but it's likely just due to what we'll mention later on below, that, Docker probably set your FORWARD chain to default DROP all packets, so nothing on your bridge ever makes it out........