If Google has determined that censorship is evil, but an open society is a noble goal, then "Do no evil" would prevent Google from collaborating with censors under any circumstances. "Don't be evil" would allow collaborating with censors if Google believed that collaborating with censors was the fastest way to inducing a closed society to open up (or some other greater good).

Not Google-specific, but:

Do no evil = "No, we are not going to torture these prisoners of war, period."

Don't be evil = "It's OK to waterboard them a little if they deserve it. Remember, we are the good guys, we're here to help."

(See also: rationale for the My Lai Massacre. Very similar thinking, it's possible to excuse awful things when you're the hero(es) of your own (indoctrinated) narrative.)

Other reasons are because people are really good at rationalization and at cognitive dissonance. Google does plenty of borderline-evil stuff, but as long as they can shrug their shoulders and say "well, it's not like we're evil, just some of the stuff we do is" then apparently it's ok.