Leia used R2-D2 and C3P0 to send a message to Obi-Wan Kenobi. R2-D2 was the primary astromech of Luke Skywalker. In Star Wars: Rebels, Bail Organa used R2-D2 and C3P0 against the Empire. Both droids always danced in rebel base and traveled with our heroes.
All this is despite the fact that C3P0 was designed by the first hand of Emperor in his childhood, and R2-D2 was his primary astromech and a friend of his? Couldn't this increase the probability of identity sabotage? Other than that, why would you trust those droids which were so close to the enemy? And, why couldn't they buy or pick a new shiny latest astromech and translator droid?