In Hunter: The Vigil, the Loyalists of Thule are a group of monster hunters who strive to atone for the fact that some of their old ideals influenced the Third Reich, and that some of their people even participated in the Holocaust. They've maintained this as their sole and driving purpose for sixty years, and completely avoided any rise of Neo-Nazi sympathies within their ranks. How? By brutally murdering any member who so much as suggests that the group might not need to obsess over the whole Nazi thing quite so much.
In Magic: The Gathering, colors across from each other on the color wheel are philosophically opposed, but there are often surprising similarities. A card which made all creatures unblockable would be blue while a card that made all creatures unable to block would be red, despite those two having the same mechanical effect.
White and Black tend to be the most egregious examples. Both handle lifelink, both have a similar keyword pool, both deal in religion, albeit through different lenses. Needless to say, the most blatant mirror cards (White and Black Knight anyone?) tend to cross this pairing.
Black also has some interesting things in common with its other rival, Green. They're the most common places to find the abilities of Regeneration (recovering from lethal wounds) and Deathtouch (venom that can prove lethal even with a scratch).
Just so the other three enemy color pairs don't feel left out: Both blue and red mess around a lot with instants and sorceries, redirecting them, copying them, you name it. Both red and white work on the premise that the ideal tactic is to take a large army and give them a common goal, and tend to be aggressive. Blue and green are probably the least alike, but both like to take creatures and make them better - although blue changes them For Science! and green changes them as a form of natural evolution.
A recurring theme in Exalted. Several paragraphs are needed to explain it.
At the dawn of time, Creation was made and ruled by the Primordials. The Primordials were tyrannical Eldritch Abominations that scorned the beings they created and were too addicted to the Games of Divinity to care about maintaining the world or protecting their 'toys.' Because of this, the gods wanted to overthrow the Primordials- but they were hardwired not to attack their makers, so they sought out heroic mortals and empowered them with Exaltation. The Exalts defeated the Primordials, and the Solar Exalts- empowered by the strongest god of all- began their unquestioned reign over Creation. But they grew greedy and arrogant, consumed with power, and fell into evil, becoming tyrants akin to those they had slain.
So the Sidereal Exalts, who saw the dark future Creation was heading towards, masterminded a plan to usurp the Solars and end their rule. The plan went off without a hitch, and soon the Sidereals held the reins of power (since the Solar-supporting Lunar Exalts had also been killed or virtually exiled to Creation's fringes.) But an ancient curse prevented any mortal remembering that the Sidereals even existed, so the Sidereals handed most power down to the Terrestrial Exalts.
The Terrestrial Exalts established a mighty empire from which they ruled Creation, and for a time, all was at peace. But eventually they grew selfish and entitled, turning away from their responsibilities to bicker and steal in the hopes of garnering political power. Their leadership became more and more divided, their army split...and their great Realm became ever smaller, assaults by the Deathlords and Fae fragmenting it.
The gods, too, became lazy and proud, abandoning those who depended on them to play the Games of Divinity eternally. The Lunars were too afraid to come back to the millions of humans that needed their protection just to survive. And the Sidereals became cold and detached from humanity, their government splitting. In the midst of all this, the Solars returned, reincarnated with the same power- and flaws- that had led to their demise. No one knows what they will do.
So it goes- Primordial to god, Solar to Sidereal (and Abyssal), even Lunar to Terrestrial. The Exalts were created to be heroes of Creation, and that is still the bulwark of their nature- but in Exalted, a hero may be no different from those he fights. The narration makes it clear that no one is blameless.
Expect this to come up in stories where the Tau Empire and the Imperium of Man are on opposite sides. Both sides are characterized by Realpolitik, and both sides are convinced of the superiority of their virtues over the wrongness of the other, each holding its adherents to an impossible ideal. Sometimes, this is even brought up by the characters themselves, with the Tau using this as proof that any human can abandon the brutal dictatorship of the Imperium and join the Greater Good, while the Imperials use this in turn to cynically point out that the two empires are Not So Different and the Imperium is at least honest about its own darkness. In the Ciaphas Cain novels, the protagonists, an Imperial Guard platoon, meet a mirror in a Tau Fire Warrior squad and the two are surprisingly quite co-operative.
Also, the Imperium and the Eldar. They're both elitist xenophobes with a smug superiority complex, they both once had great empires that were brought low by Chaos, and they're both now slowly dying out and beset by enemies on all sides, bitterly fighting for survival. Also, there's what Inquisitor Kryptman did to avert a Tyranid assault (lure it into Ork territory), which is little different than what Eldrad did to avert an Ork invasion (lure it into Armageddon).
And of course, Space Marines and Chaos Space Marines, as Evil Counterparts to each other, would have to qualify. All Space Marines are enhanced into killing machines and tend to default to violence as a solution. Many Space Marines and Chaos Marines are deeply religious, yet serve a cause that could easily be considered evil. Many on both sides believe they're fighting for the good of humanity, although how they define that tends to be rather unpleasant on both sides.