R2-D2 is one of the most iconic characters in Star Wars and arguably the greatest robot in cinema history. His antics and memorable interactions with C3PO add charm and comic relief to this science-fiction epic; however, there is a huge plot hole in this saga involving Artoo that not even Mark Hamill can explain. While Artoo was Anakin Skywalker's personal droid in the prequels, he never bothered to reveal to Luke Skywalker the truth about his father. C3PO had his memory wiped at the end of Episode III: Revenge of the Sith, but Artoo's memory remained the same throughout all three trilogies.
While George Lucas and company probably never envisioned R2-D2 having a significant role in the events before Episode IV: A New Hope, Lucasfilm decided to add the famous droid and his companion C3PO to the prequels despite it not making logical sense. Their minor cameo in Rogue One is one thing, but C3PO and R2-D2 being key characters alongside Anakin and Obi-Wan Kenobi is another thing entirely. Obi-Wan even states in Episode IV, "I don't seem to remember owning a droid," when he meets the duo despite being around them so often during the prequels.
This seems like a huge plot hole, but there are reasonable explanations behind why R2-D2 never reveals the truth about Anakin. In Revenge of the Sith, R2-D2 accompanies Anakin to Mustafar on his mission to assassinate the leaders of the Confederacy of Independent Systems. By that point, Anakin is anointed as Darth Vader by Emperor Palpatine and has killed members of the Jedi Temple; however, R2-D2 is unaware of Anakin's doings and continues to follow him.
Anakin orders his droid to stay with the ship once on Mustafar; therefore, he fails to see any of the events that condemn Anakin. In the scene where Padme Amidala confronts Anakin, both Artoo and C3PO, who accompanied Amidala and Obi-Wan to Mustafar, are out of sight, and during Obi-Wan and Anakin's duel, they remain missing from the picture, so it's safe to assume R2-D2 didn't witness Anakin's near death experience nor his survival.
Everyone who survived Order 66 also assumed Anakin perished with them except for Obi-Wan and Yoda, so R2-D2 would most likely not have been be informed by either party that his former master was alive and now living as Vader. When considering the fact that Artoo and C3PO were later entrusted to the Organa family, it makes even more sense that neither droid would be informed about this, but one question still remains. Why wipe C3PO's memory but not Artoo's?
It is not common for non-droids to speak Artoo's language, so there wasn't much of a concern about the Organas and Leia understanding his account of the prequels, even though C3PO is with him. While C3PO can understand his droid companion, with his memories of the prequels wiped and his skepticism of Artoo's words, C3PO would most likely not believe this wild story.
The only other character who communicates with R2-D2 is Luke. In the Dagobah system, Luke appears to interpret R2-D2's beeps and buzzes like a dog's bark instead of actual words, so once again that concern of Artoo spilling the beans isn't a real issue. However, if Luke truly knew what Artoo was saying, it wouldn't have impacted his journey too much.
Luke did not directly interact with Darth Vader in A New Hope, meaning he wouldn't have time to tell Vader the truth if he wanted to. Meanwhile, in Empire Strikes Back, Luke refuses to believe that Vader is his father. If Luke is not willing to believe Vader himself, the chances of him believing a droid's claims when no one else outside the villain is willing to verify them is unlikely.
When Luke finally accepts the truth, he makes it his mission to redeem his father, a task that's completed in Return of the Jedi. If he were to learn from Artoo the truth earlier on, then he could have been more susceptible to his father's overtures in Episode VI. Instead of Obi-Wan and Yoda being his guides, Vader potentially would have taken that role; however, Luke's morals are so strong, and the outcome of the classic trilogy would have likely been the same regardless.
If anything, Luke learning about Vader from R2-D2 would have at least spared him from pining over Leia, who turned out to be his sister. This also raises a bigger question, which is what if Leia found out who her parents really were from R2-D2? The events of the entire original trilogy would have been altered to the point where Leia could've became the main Jedi trainee instead of Luke.
For this reason it makes no sense for Bail Organa to wipe C3PO's memory while keeping Artoo's intact since they were around Leia while she grew up. Bail's small but key role in Rogue One shows how much influence he has on the events of the original trilogy, so in his eyes, keeping R2-D2's memory in tact wasn't much of a concern, and the Star Wars saga shows he was right not to worry.