Bingowings said:

I can see it making sense that Red Leader would let Luke fly when the planet they are defending is about to be blown up but not making sense to send a gold, loud, fussy butlerdroid into a bunker siege situation on a green planet.

C3PO being part of the mission comes down to one simple thing. There is only one simple "if" involved and that is if Solo decided so (he was strike team leader). Judging from some of his past decisions (foolish charge on Strormtroopers, not paying Jabba for 3 years, etc.), it is not too hard to believe he approved this one too.

On the other hand, Luke flying X-wing has tons of complicated "if"s: if rebels had a spare X-wing, if rebels really didn't have spare pilots to fly it (highly unlikely), if rebel command is willing to take some unknown farm boy, if Luke's "crop duster" management skill is anywhere near sufficient to handle an "F-16", and so on.