My understanding (feel free to enlightenme if wrong) is that most distros still offer other init systems, they just aren't requiring package maintainers to suppor them. Thus.. things you want to use might become dependent on Systemd.
Also (as far as I know) Gnome is the only thing already doing this with KDE likely to follow soon.
I'm guessing (more speculative) that Systemd dependency is only likely to be an issue with big "desktopy" projects like this.
I hope that you are not running Gnome or KDE on your router!
So... what's the problem? Just use a different init!
Also... what kind of router are we talking about? Is this a PC being used as a router? Or is it a device which was actually meant to be a router. If the latter what distro does it run? Do router distros like openwrt, ddwrt, etc... actually use the same init systems as desktops? I always assumed they just ran a few simple scripts.
That being said.. although I've been a long-time Linux user I am using M0n0wall myself. It's a BSD based router distro, much like Pfsense which others have recommended but a bit lighter. I only chose it b/c it (and pfsense) supported the device I wanted to convert to a router and I didn't see anyone mention any of the Linux ones for it online.
My only complaint is that I haven't been able to get a VPN server running on it. I'm not sure this is M0n0wall's fault as this has been a problem for me on a number of other installations I have attempted. I suspect my cable company of blocking it.
But, anyway.. not a single device in MY home seems to care if it's packets are being routed through Linux, BSD or whatever! How about a Syllable router for the win?!?!