Why is C-3PO kept in the dark in Return of the Jedi while R2-D2 is not?

Question

In Return of the Jedi, the beginning sequence shows C-3PO and R2-D2 making their way to Jabba the Hutt's palace. They are sent there to bargain for Han Solo's life.

When the negotiations with Jabba begin, R2-D2 shows him a message from Luke Skywalker. In that message he offers the two droids as gifts in exchange for Han Solo. To which C-3PO says:

C-3PO: You're playing the wrong message!

So C-3PO is obviously very surprised that Luke has just said this.

Then, on Jabba's barge, we see a plan play out that Luke Skywalker has already put in motion.

We see C-3PO bump into R2-D2 and warn him that they are about to kill Luke and that they might be next, but R2-D2 says something which C-3PO responds to by saying:

C-3PO: I wish I had your confidence.

So this just reinforces that R2-D2 was in on the plan as he was also preparing Luke's lightsaber to launch it in the air to where Luke was on the smaller craft.

The only way for this to have played out was if Luke had given his lightsaber to R2-D2 before they were sent to Jabba's palace. This is obviously the case since Luke did not have his lightsaber while being captured at Jabba's palace.

So R2-D2 had to have known details of the ensuing plan, but as we can C-3PO did not.

Why was C-3PO left out of the plan?

Answer 1

This is addressed in the new (Disney canon) junior novelisation for Return of the Jedi.

So it was up to his closest friends:
the loyal and hairy Chewbacca,
the not-always-so-loyal Lando Calrissian,
the farm boy turned star pilot Luke Skywalker,
and the rebel princess Leia Organa
to come up with a better plan.

A very risky, very dangerous, very easy-to-go-wrong, very unlikely-to-work sort of a plan.
The sort of plan that was so unlikely to work, in fact, that C-3PO would never have agreed to be part of it.
So he wasn’t told.

_{^{Return of the Jedi: Beware the Power of the Dark Side!}}

Answer 2

He talks too much, tends to ramble, and to get scared/excited easily, so he might've let something slip, and give away the plan. So they didn't tell him, and as a plus, the act was more convincing, with him all scared.

Answer 3

I think the reasoning was twofold: because 3PO probably would have given it away (as has been explained pretty succinctly by Valorum), and because so few characters are able to understand R2's own speech that there's virtually no risk of the little droid giving it away himself. So instead of leaving both droids in the dark and making plans some other way, R2 was the perfect accomplice.

Answer 4

This is addressed in Legends in the Return of the Jedi radio drama.

LEIA: Threepio, are you all right?

C-3PO: Well...

LEIA: I'm sorry we couldn't let you in on Luke's rescue plan, Threepio.

C-3PO: Oh, I quite understand the logic of it, your highness. My memory banks are more open to scrutiny than Artoo's.

LANDO: When 9D9 scanned you and found no sign of subterfuge, it put Jabba off his guard.

_{Return of the Jedi Radio Drama, Episode 3: Prophecies and Destinies (via YouTube)}

It appears that C-3PO is not only worse at lying than R2-D2, but also has less secure electronic memory.