The core issue is that Riven isn't portrayed as a traditional Noxian, or a radical/believer of any kind. She's stuck in this pity-pot mode and 16 year old anime girl angst that buries most of the intrigue her character is based on.
This.
Riven is essentially a foil to Darius - Both have the same 'Might makes right' beliefs, both believe in 'Strength above all,' and both are professional soldiers who see nothing wrong with killing. Riven wouldn't get along with Demacia any better than Darius would (though Darius and Shyvana might find some common ground).
What differentiates them is how they reacted to hypocrisy.
Riven melted down just like her comrades, only her meltdown was mental rather than physical. That one very personal instance of betrayal was enough to break her. She couldn't believe that was possible and saw the corruption everywhere she looked rather than seeing it as an isolated incident she could potentially do something about. She ran away and began moping around in that cute little self-imposed pity-party that makes people want to hug her and adore her and fetishize her. Just remember, she's fighting for redemption, but the society whose eyes she seeks to redeem herself in isn't all sunshine and rainbows and the future she wants to build resembles Wolfenstein The New Order more than Equestria.
Darius, presented with the same situation, looked his commander in the eye, said 'Nope,' and gave him a fatal case of axe poisoning. He's willing to work within the system, take action against the problems he sees, and try to fix it from within. That's part of why he doesn't like Riven - Not only does he see her as a traitor but he sees her as a weak-willed pansy because she ran away from her problems rather than fighting them.