In the new canon novel Star Wars: Bloodline, Leia's family secret is exposed in senate, and the news quickly spreads across the galaxy. In an instant, she loses all credibility, and everyone suspects her - and even Luke - of being evil. While I do understand the widespread shock, and the hatred of Vader, I can't quite grasp why the senate turns on Leia so quickly and violently.
She had previously been the most widely respected member of a deeply fractured New Republic senate, entirely because she had been such an important part of destroying the Empire. The senate, divided into Populists and Centrists, had been fighting for years, and the only event that had managed to bring them together in recent years was the dedication of a statue of Leia's adoptive father, Bail Organa, outside the Capitol Building.
Consider her history, in pros and cons:
Biological daughter of Vader
Didn't tell anyone she was Vader's daughter
Vader's sole positive contribution to her upbringing was his role in her conception. He had no part in raising her.
Biological daughter of Padme, virtually the only senator who resisted Palpatine's power grab.
Raised by Bail Organa, one of the founders of the Rebellion, and one of Vader's worst enemies.
Spent her life fighting against Vader and the Empire.
Played a vital role in the destruction of BOTH Death Stars - stealing the plans for the first one, and shutting down the shield generator for the second one.
Met Vader exactly three times:
The first time, he tortured her, blew her planet up in front of her just to be mean, and sentenced her to death.
The second time (in the comic books), he tried to capture/kill her.
The third time, he tortured Leia, along with her future husband and their Wookiee friend, then froze her future husband in carbonite and gave him to Jabba the Hutt.
Commanded the Rebel forces on Hoth, and led a successful tactical retreat when the Empire attacked the base.
Killed the criminal warlord Jabba the Hutt with her bare hands (and a chain).
Her brother - also Vader's biological child - and her future husband blew up the first Death Star.
Her brother is believed to have killed Vader and the Emperor.1
She didn't even know that Vader was her father until a few hours before he died.
This is a very one-sided record, and one that demonstrates that Leia has done two things wrong: Being conceived by the wrong guy, and not telling people he had conceived her.
So why did almost everyone - including her political allies and friends - turn on her simply because her dad sucked, despite the fact that she clearly despised Vader, and Vader clearly wanted her dead?
1: From Star Wars: Bloodline:
“How dare you question him?” Leia knew her voice sounded too sharp, too shrill, but her temper had gotten the best of her. “After everything Luke’s done for the Rebellion and the New Republic? Maybe Lady Carise has forgotten that he was the one who destroyed the first Death Star — or that he was responsible for ridding the galaxy of Palpatine —”