If there are no pressing territorial reasons for conflict, then that takes out an awful lot of possibilities. Historically religious and dogmatic reasons for conflict were little more than trumped-up excuses for either political or territorial reasons. Have a bunch of nobles that you think might cause you political unrest? Time for a Crusade! send them off to The Holy Land. Want to annex a neighbouring state? They're keeping us from reuniting with our traditional brothers!
You can go the religious route, but then you have to support it with pure dogma. From Here 'Til Underverse Come!
You can go the ancient technology route, but that's just substituting what your "scarce commodity' is. I used this in an old Space Opera RPG campaign, pre-Babylon 5 by a decade or more. A trope is still a trope, even when you change the window dressing.
There is something that you can do with tech, however. Different species aren't necessarily going to develop a given tech at the same time. Conflict could arise if one species withholds effective tech from another. More efficient drives that reduce fuel use. Better oxygen or waste recycling tech. Artificial gravity. You can't go too far, though, or any conflict would be over in seconds. The Minbari easily rolled up any human defence right up to the Sol system, barely breaking a sweat. If drives and weapons are TOO much out of scale then it's tough to maintain the conflict, unless the more advanced race is pacifistic to a fault.
Edited for crappy spelling
What if it isn't ancient technology, but "modern" technology.
The Ascended Federation has the most advanced technology in the known universe (and the ascended Federation has explored more than most).
The other human colonies weren't as successful. The Federation has relatively strict non-interference protocols, because it believes others should only attain such technology if they are "ready" for it. That might be an "holier than you" attitude or something actually based on hard-won experience, but either way, they are not sharing. Their policy also means that they will never seriously hurt any of the "lesser" people. They will likely blow up a station or ship that comes under control, but only if they can minimize the loss of life.
But the tech they have is really awesome. Drugs that provide practical immortality, allowing century old humans to eventually achieve mastery of mind over body, allowing them to ascent into a higher plane of existence. Programmable matter that can be turned into anything. Most of the stuff might have the limitation that it is still used up, the real jackpot would be taking over one of their industrial fabber ships or one of their colonies, but that is practically impossible, because the Federation defensive tech at full power is utterly impenetrable.
The "lesser" colonies of man are trying to get access to whatever they can. Maybe some Ascended Federation freighter full of programmable matter got lost in an ion storm. Maybe somewhere a young member of the Ascended Federation rebelled against their non-interference policy and dropped some drugs to help a colony in need to deal with a terrible plague. Maybe an old communication satellite or observational satellite was discovered and cold provide access to their instantaneous FTL communication or observational abilities.
It is still a fight for rare resources, but there is also dogma involved:
Some people believe the Ascended Federation are basically living gods in space. They believe that the Federation will share its technology once everyone has agreed to stop stealing and using it, and collect it for safe-keeping, possibly returning it to the Federation even.
Some people believe whatever they find must be put to immediate use. Past attempts to understand the Federation's technology have mostly failed or brought only little advanced - if you have a ton of programmable matter, turn it into something useful. If you have some medical nanites that can cure a plague, use it on the next chance you have.
Others think you should study the artifacts and learn how they work.
And yet others believe that the Ascended Federation's technological gifts are temptation that leads to the people fighting each other, instead of working together for a greater good.