Comment 4 for bug 1698023

Please don't do that.

resolv.conf is a symlink to /run/systemd/resolve/stub-resolv.conf and should remain that way -- this makes sure any changes on the network are reflected "automatically" in the resolver's behavior, since you'd be asking systemd-resolved rather than the libc resolver, and it already knows about the contents of /run/systemd/resolve/resolv.conf.

If you must use global nameservers, you can certainly modify /etc/systemd/resolved.conf's DNS= field to add them, but be aware that "global" nameservers don't make all that much sense. Nameservers are per-interface, because they might not be reachable by all interfaces when there are multiple connected.