The rebels were fighting for democracy. Although the senate wasn't dissolved until be beginning of EP4, I think it is reasonable to assume the senators were basically appointed by Palpy at that point. Once the Death Star was complete he decided he didn't need them anymore.
I always had the sense that the Senate was the only check on Palpatine's power, the one thing that kept him from being an absolute dictator, so that things weren't as bad as they could've been. He dissolved the Senate precisely because they weren't just a rubber-stamp legislature but an actual force of opposition. Keep in mind that Leia was herself addressed as a Senator in the original movie. Perhaps the Rebel Alliance was originally more of an opposition party, but as Palpatine came closer and closer to dissolving the Senate and seizing absolute power, senators like Leia began organizing it into a resistance force so they could fight back if they proved unable to ward off the Senate's dissolution.
Drawing on the EU for a moment, there is a revealing scene in "Dark Lord" where Palpatine/Sidious meets with some Senators and essentially tells them that HE and HE ALONE is in complete control and essentially tells them that while they can talk, debate, etc., HE makes all of the final decisions and warns them not to introduce amendments, motions, etc. challenging his decisions. The "Democracy" of the Old Galactic Republic basically ended the moment that Palpatine announced his ascension to Emperor and the Senate cheered him on. The Senate, at that point, was rendered about as potent as a Debate Club. He was also in the process of tracking down and arresting (and probably killing) the 2000 (?) Senators whom signed a petition in ROTS (deleted scene) asking him to cede his emergency powers once the Clone Wars ended.