I have been told by someone in a position to know that Sen. Lieberman was told by his rabbi NOT to wear a yarmulke in public because people might mistake his public statements for that of a rabbi, which he is not.
This may sound silly but when I travel outside the NY area to parts of the country where there are few Jews lots of people assume that the fact I wear a yarmulke means *I* am a rabbi, which I am not.