So, from what I understand (this might just be a headcanon from my regular pod of players), the highest ranked Immaculates know the truth that the Solars are the Solar Exalted, chosen of the Unconquered Sun. But they also know that, for whatever reason, the Solars go mad if they hold their power, and so they must be culled. This is something that's only really told to the most zealous and high ranking monks. Others - including ordinary citizens - are told that the Solar and Lunar Exalted are demons that stole their power from the sun and moon and take over the body of their host.
But in both cases, they're also told the power is so immense and extreme that it corrupts the soul of the wielder. At first, a Solar or Lunar may seem like a good person with good intentions, when their soul is at its strongest and the demon/exaltation is at its weakest. In their early days they may even do some real good! But the longer they're allowed to exist, the more corrupt they will grow, the more evil they'll become, until their power undoes everything good they might have done and destroy all they hold dear.
It's like the Dark Side from Star Wars. Start out with good intent on the dark path, but before long it will destroy you and everything around you. Except *every* Jedi, without exception, eventually turns into Sidious/Vader. It's not their fault, but they have to be put down for the good of all.
I like this variation moreso than the idea that the Immaculate Faith is an outright lie. There's some real weight to it, and while there is a lie in where the Solars came from, the reason the Immaculates have to hunt them down is true and righteous (at least in theory). The truth feels less like a "aha everything you believed in was a lie", and more like a "okay it's more complicated than we say to the public". Which is fair.