I would like to point out that the way the rebellion worked, according to my understanding, is that there were a lot of various cells of rebels that were largely cut off from each other and organized through a network of middlemen. That way if one cell was compromised, the whole organization wouldn't be in jeopardy. Your PCs, presumably being new to the rebellion, shouldn't have any particularly damning information, such the location of a major rebel base, until they have proven themselves loyal and reliable to the rebellion.
That being said, as others have suggested, if the players are questioning working for the rebellion, I'd have a talk and discuss whether you should be playing EotE.
Oh, but they have some pretty vital info; namely the location of thirteen solar systems hidden away in Unknown Space holding many civilians. It's the reason they got in the Rebellion, because these 'colonies' as they're called joined the Alliance.
And yeah, I've asked them, and they mostly want to stick to their current characters in the current situation. (The options were continue as is or make new characters, since I don't- and never will- like the idea of the characters being able to ditch the Rebellion, especially when that would be very, very, very bad for the Rebels.)