As to the Gith - I think that "every evil must be destroyed right away, slash slash!" is a pretty stupid creed, so if your lawful char has 6 INT it might be actually a good choice
If you want to go with the "enemy of my enemy", then you have to think whether only being at war with the illithids is enough to get favours from surface people? I'm not so sure about that. Frankly, while Mind Flayers are disgusting, inhumane and horrible, a well equipped party can eradicate a whole city of them, and once you protect yourself from their mind powers they are just another type of monster.
I find the drow much worse, because they chose to be such massive jerkasses (and because they are a stupid concept, not to mention tailored, as a race, to prove that a society where women aren't inferior will invariably become a nightmare