As you sort of mentioned you have to choose between your resolv packages.
In the case of systemd-resolved+systemd-resolvconf I set it with the following:
/etc/NetworkManager/conf.d/dns.conf
[main]
dns=none
Then link the resolvconf:
ln -sf /run/systemd/resolve/stub-resolv.conf /etc/resolv.conf
And then set your custom DNS
/etc/systemd/resolved.conf.d/dns_servers.conf
[Resolve]
DNS=1.1.1.1 1.0.0.1
Domains=~.