I think you guys are getting a little too philosophical.
The Sith and Jedi orders are nothing more than organizations made up of certain individuals.
As long as other members of the organization recognize you to be one of them, you are a Sith/Jedi. Alignment has nothing to do with it.
Of course, if the other Sith actually KNEW you are secretly following the light side, then they'd probably kill/banish you, but as long as you manage to prevent that, you are a Sith.
^This. If one specific Dark Side Jedi in the past would have won on Tython, the Jedi would be a Dark Side organization and still be called Jedi.
There are light side Sith, but they are (normally) considered as heretics by the other Sith. In religions, heretics are normally still considered as part of the religion, but as people who got it wrong and must be stopped. And "stopped" means "killed" in the Sith order.
There are at least two points where you see that in the game:
1. On Korriban: An Inquisitor asks you to kill some heretic acolytes.
2. On Dromund Kaas: You find the teachings of a light side Sith (his holocron) in the Dark Temple.