I noticed that tailscale magic DNS appears to not be able to understand that /etc/resolv.conf doesn't need to be manually overwritten when using dhcpcd whereas there is no such problem when using the ISC dhcp client.

Obviously, tailscale is in the wrong for trying to infer whether or not /etc/resolv.conf is under system control rather than just providing a knob to tune that behavior but that doesn't change the fact that my DNS gets subtly broken when using dhcpcd.