One of my favorite bits of the Thrawn trilogy was the New Republic having to cope with the fact that one of their ships, shot down early in the war, poisoned an entire planet, and that the Empire was the one providing aid in the aftermath.
Although it's later revealed in The Last Command that said space battle took place something like 50 years prior, which put it firmly into Clone Wars era, not Empire/Rebellion era. But yes, until that revelation, they still had to deal with the concept that the Empire had supposedly actually done some good.
I think I read somewhere that Saw Gerrera, who appeared in The Clone Wars TV show in season 5, was definitely considered an extremist and had had a break-up with the Rebellion due to said methods.
'Nother topic, I just finished (last night) reading the (now-Legends) "Legacy of the Force" novels, and it was really, really neat to see Darth Vader in Rogue One open up a can of Sith on the Rebel soldiers while at the same time reading of similar scenarios performed by Darth Caedus (do NOT Google that name if you don't want massive spoilers).
Kinda looking forward to the day when they make a rated-R SW movie. Lightsabers both cleave and cauterize simultaneously, right?