This is sort of a logical extension of my earlier comments about looking at law vs. chaos in term so moral relativism. A lawful character is more likely to be close-minded, or at least set in his or her ways, whereas a chaotic character is more likely to be open-minded or willing to entertain different points of view.
Note, this doesn't have to mean that a lawful character would look down on people with other points of view, or that they'll feel compelled to push those views onto other people. Both of these traits could be excellent for a lawful evil character, and could still be played will for even a lawful good character, but I don't feel that they're necessary. For example, if we apply this to religious beliefs then a lawful character could just as easily be praying for people to "see the light" as he or she would be to go about actively proselytizing.
On the chaotic side, the character is more likely to be accepting of different beliefs and points of view. Taking the same religious argument, then a chaotic good character could very easily still see the good that is done by believers of other gods and see them as kindred spirits, even if they don't follow the same god.
Similarly, a lawful character is more likely to hold to their beliefs more strongly and feel more threatened if they are challenged, whereas the chaotic character would be more likely to hear the person out and be swayed by their words.
This doesn't have to mean that a chaotic character can't have strongly held convictions, it can simply be a matter that they see those as their own personal convictions and they see how they might not necessarily work for everyone.