Kanan and Ezra are part of the Jedi religion and Force tradition, the Rebel organization, and the Phoenix squadron.
Asajj's religion and Force tradition is Nightsister.
A Baptist who teaches at a Catholic school is still a Baptist. A Nightsister who works as an assassin for a Sith is still a Nightsister.
As to putting the Rebel tag on the young Rex we already have in the game, that design philosophy just completely breaks down the game. Factions are designed to work together. Start putting tags on people arbitrarily and it breaks down game design. Blur the lines between factions too much, and it becomes much more difficult to design a game, and there are a lot more unexpected interactions. Especially since every time a novel, movie, or TV show comes out that reveals more about a character's backstory or future, you have to put more tags on them. For the logic you present to be internally consistent, they would have had to put the Empire and Imperial Trooper tags on all five Han Solos once Solo revealed he used to be an Imperial Trooper, regardless of design or interactions.