For Carrie I think they had the blessing of Billie Lourd who of course played a supporting character in the trilogy, and even stood in for her mother in ROS's flashback scene (The lightsaber duel with Luke & Leia).
It's a bit easier for the masked characters I think. RD-D2 Fett, Vader, and Chewbacca are all played by new actors or effects although that's been the case for a while. Even in the original trilogy, Prowse-despite his insistence-was not the only Vader actor in the suit, as there were some who did the fighting and even a hand/glove double for a few scenes when that was all the shot needed. Jeremy Bulloch also wasn't Fett in the new special edition shots but some ILM shots.
I think Anthony Daniels has somehow done 3PO and his voice at pretty much every appearance in suit except probably a few video games and the TPM puppet (although funny thing is, when AOTC tried filming some scenes with puppet 3PO, it was actually Daniels puppeteering him, but they decided to ditch that and just give us the covered Threepio). Although he's nearly 80 so I'm not sure if he'll do that much longer, or at least switch to voice-only.
Interesting thing about Palpatine, Ian was only brought back for Rebels/Bad Batch in part because Ian Ambercrombie had passed away and Tim Curry had a stroke.