The two things are not mutually exclusive. By believing in God, I don't abdicate responsibility for my actions, thoughts and speech. On the contrary, I feel my beliefs give me a stronger responsibility over those things. However, I also believe that I am incapable of anything good of my own accord and only by the work of Jesus Christ within me.
Side note: Donald Knuth is also a Christian. You can read some of his musings in "Things a Computer Scientist Rarely Talks About", a sample of which is publicly available. (Unfortunately, I haven't yet devoted the time to read this myself, so I wouldn't consider this an endorsement.)
They take responsibility for their own actions, thoughts and speech.