You can install one without regard to the other. I have two machines running X/9.1 and one I installed in one order, the other I did the other way. I honestly couldn't tell you which I did which way, but both work fine.
I do recall that the end result was a little different, as one thinks it's right and moves the other's stuff, where (I think) 9 just puts itself in at the root and doesn't move anything. If you install 9 after X you end up with more silly crap in /
Anyway, don't let all of the newness fool you, the old macOS is still the old macOS. A dragged system folder from another machine will work as well as it ever did. Booting from other drives / other system folders on the same drive or partition works wuite well. If you're scared, you can install a clean version of 9.1 and pcik which one to boot from.
Here is what I did:
I have MacOS 9.1 on a separate partition, only the MacOS 9 base (and a few office & netscape prefs).
You dont have to have OS 9.1 installed on the OS X part of the hard drive in order to work.
Just go to any OS 9.1 machine that works well and copy the system folder. Then just reaplce your old system folder with the new system folder and customizze it as much as you want.
I now have several installs of various 9 flavor OS's all over the place. 5 9.x installs and 1 X.0.2 install within 3 drives. I pick which one to boot from at any given time, and it happens. still, it's all good.