The Major Race/Minor Race business is the equivalent of the Council Race/Non-Council Race divide from the Mass Effect games. It's a matter of politics and perceived status, whatever other justifications are made for it, and it defines the setting around what the big players -- in this case the Vilani -- want normalised (much of which is, their own hegemony).
It's actually sort of comedic in its way. The Vilani just want everyone to stop doing the equivalent of sticking random things in their mouths. It's ingrained in the people of Vland that you only put something in your mouth if it has been correctly worked on by experts, confirmed by precedent, and catalogued correctly. Otherwise you just poisoned yourself. People working outside of the lines and doing their own thing is unsafe, perverse, and an affront to the ancestors, whose correct action ensured your prosperity. Vilani social institutions are effective so long as the system is closed, so inevitably once their universe encompassed other races all those aliens had to be wrangled into conformity. They needed an excuse to justify imposing on everyone, so they came up with "had interstellar reach" and then tweaked it to exclude the Geonee and Suerrat.
Mission accomplished (with the help of a few Consolidation Wars).
Only, over the millennia, they've had to accept other races as "equals" because they turned out to meet that one specific criterion; the problem for the Vilani is, none of them do it *right*. The Solomani and Vargr are barbarians who merrily rampaged across the lawn and can't organise to save their lives -- Ramshackle Empire, the Vilani sneer, and the Vargr don't even get that far; the Hivers and K'kree don't actually care about these Human political concepts, since their empires are just a managed anarchy and a singular herd/crusade respectively; the Droyne don't even have an empire (and if Chirpers are Droyne that means Vilani are arguably in the same category as *them* -- oh, how the mighty have fallen, victims of their own obsessive categorization!). The Aslan are a young race even before the "actually didn't invent the drive" revelation. Only the Zhodani get it "right" and behave "sensibly" from a Vilani viewpoint -- and, final irony, they're the one polity the modern Vilani are politically *unable* to respect, because of the Psionics issue and all the cultural/ethical disagreements it's tied up in. (One does wonder if another factor in the Imperium's anti-Zhodani stance is the fact that the Vilani cultural mindset cannot abide a competitor -- not merely in a political sense, but in the form of something more threatening; a claim to a stable, centralised, organised system that might actually be *more effective than theirs*).