Comment 5 for bug 1778073

I run into this bug and found the cause:
When starting dnsmasq, a call to resolvconf is made to update the server entries. If postfix is installed, the /etc/resolvconf/update-libc.d/postfix script is called which tries to reload it.
The problem is that dnsmasq is a nss-lookup.target, while postfix requires nss-lookup.target to be active in order to restart. That will create a deadlock, the ExecStartPost=/etc/init.d/dnsmasq systemd-start-resolvconf script in dnsmasq times out and the service is not started.
This is only triggered by having dnsmasq and postfix installed. If you also install nfs-common, the rpc-statd will also be part of nss-lookup.target and it won't be triggered.
I hope somebody will find this useful, took me days to debug it :D