The game manual says that you can get C3PO to stop talking by hitting the ESC key or clicking the left mouse button. So far, that doesn't seem to be working.

How do I get that droid to shut up?

I searched through the threads and found the solution here:

https://www.gog.com/forum/star_wars_rebellion/skip_intro

In short: rename the ALBRIEF.DLL and EMBRIEF.DLL files in the game files. Works like a charm.