He positively HAD his memory wiped in the end of episode III

Easy: 1. he didn’t know Anakin survived 2. he got reprogrammed to „forget“ everything about Luke and Leias birth and they made him unable to tell anything. It‘s against his programm to tell Luke

R2-D2 (in beep-boop): Luke, you are the son of Darth Vader. Luke: That's right, Artoo. We're going to the Dagobah system R2-D2: And C3PO is your brother. Luke: Sure, we can get some fries on the way.

Serious lore answer? The droids don't know that Vader is Anakin, that's all. C3P0 had his memory wiped at the end of Revenge. As for R2, he knew Anakin turned to the dark side, but he did not know that Anakin survived and was turned into Vader.

Because the prequels were rushed and not thought out

What I recall from the films: R2 wasn’t near the duel between Obi and Anakin, so could only assume Anakin had died on Mustafar. The most he could have told Luke is that his dad became a bad guy and died in a fight with Obi-Wan. Obi-Wan even thought Anakin had died and didn’t find out he survived and became Vader until later when R2 wasn’t around (Obi-Wan tv series).

The real answer is everyone just pretended to understand droids and never actually understood any of it.

He thought he knew.

Because Lucas DGAF

I’m pretty sure there’s a line in one of the movies that talks about wiping his memory tho.