Luke clearly doesn't understand R2D2 in the OT. His X-Wing has a translator, and Luke clearly guesses what R2 is conveying while on Dagobah.
Anakin also had his ship translate for R2 in the PT.
In Disney Star Wars, it seems everyone can just understand droid-speak, including Luke. You think the Republic made learning droid-speak mandatory?
You're right Luke is clearly shown unable to understand R2 as he either has 3PO translate or his x-wing digital readout. He is at best able to get the general idea of what R2 is saying while on their own.
However, I would argue Luke and R2 spent a lot of time together post ROTJ and in those years I don't think it would be a stretch to say he was able to pick up the langue to a degree that is suitable to hold a conversation without 3P0.
Astromech droids don't technically have language - "beepbeep" doesn't mean anything specific.
When they speak, they're digitally beaming the words out to be received by other machines, such as the text display in Luke's X-wing, or Threepio's electronic brain. The beeping sound is just to show R2 is sending the words out.
Evidently the current Lucasfilm group disagrees as all the main characters can understand droids now.
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