The Empire and Rebellion share the same enemies
While it seems difficult to make sure there's only one rebel group, it's easy to imagine a situation in which one rebel group is vastly predominant over other ones. In fact, there are many examples. For instance:
1. Democrats v. Republicans -- The parties may be "at war," but they both agree that third parties such as Libertarians or Marxists in power would be far worse(I'm not taking a stance here about whether that is correct). Their combined influence and agreement on this is more than enough to effectively silence third parties(though if both parties' leaders are highly disliked, a third party may gain some traction).
2. Catholics v. Protestants(in pre-enlightenment Europe)-- They may have considered each other heathens, but they both considered everybody else to be heathens as well. If there was ever a serious threat posed by a third religious sect, say Eastern Orthodoxy or Islam, they would have united temporarily(as Western-European Christians) to crush it.
3. The Kuomintang v. <PERSON> -- They were bitter enemies, but they were united in national identity. 145
Considering the Japanese to be rebels against Chinese dominance of the east(which could kind of make sense in a twisted way), the KMT and CCP united temporarily to crush the third faction, and only resumed warring when it was deemed that the greater threat to their society was defeated.
To integrate this concept with your example, I would suggest that in your world there are really only two political ideologies that have any popular support with the commoners. The first is the caste system currently in place, of course. The second is unlikely to be something as radical as democracy or Socialism, or even a republic, and is more likely to take the form of a military dictatorship by a benevolent secular ruler, a theocracy, or some kind of fragmented city-state model. It could be that your world is young enough that only two forms of government have every really been tried, or it could be that the records of previous civilizations have been lost, or it could be that your society is extremely conservative. But for whatever reason, both the Empire and the Rebellion consider any third political ideologies to be far, far, more dangerous than they consider each other, and so will temporarily unite, for instance freely giving each other intelligence about third factions, just so they can be stamped out.
Starting a third rebellion would be really difficult, and not worth the expense
1. Mac v. PC -- (This one is slightly different, and probably less applicable to your scenario). There's enough variation in consumer preference to keep people switching from Mac to PC, or vice versa, when one side slips up or has a breakthrough, but there's not enough variation in consumer tastes to justify the existence of a third for-profit competitor. Apple and Microsoft both have huge infrastructures dedicated to producing a quality product, and an upstart third OS company would not have the resources to create a product as good, and no realistic chance of gaining a large enough number of users to generate the necessary revenues to become a competitor. In essence, the market is only big enough for two, based on costs of production, and amount of variation in tastes.
Applying this to your scenario, it could be that most people don't care what replaces the current system, inasmuch as they really just want the current system gone. Hence, there would be little support for a third faction, as people would just see it as a subtraction of resources from the rebellion that could be used against the Empire(In the same way that people saw <PERSON> as just a subtraction from <PERSON> votes). Because starting a rebellion is very expensive, and everybody thinks the current rebellion is working out for them, there wouldn't be enough interest to generate a third faction. 145