Brian Wilson won't shave for the Yankees, so he won't play for the Yankees
The old school, seemingly outdated policy has brought on some interesting stories, but I can't say whether or not it has ever truly affected the team in the past. Gary Sheffield had no problem chopping off his beard before playing for the Yankees in 2004, and Johnny Damon got rid of his legendary flow when he became a Yankee in 2006.
Free agent relief pitcher Brian Wilson, however, has literally put years into crafting his massive, imposing black beard. It has become what defines him, along with his loopy personality and typically strong pitching.
The Yankees, like any team in the MLB, could always use a nice addition to their bullpen, and Wilson is one of the top relievers on the market. The Yankees were one of eight reported teams in the running to land Wilson's services, but that was before they got some off-putting news from Wilson's agent - Wilson is unwilling to shave his gargantuan beard to play for the Yankees. General manager Brian Cashman has since announced that the team will not sign Wilson.
Growing a beard is what Wilson does best. The Angels didn't ask Albert Pujols to stop hitting home runs when he came to Anaheim. That ferocious black beard is just who Wilson is, and he is too proud to sacrifice it just to play for the most decorated team in the history of baseball. If Wilson lost the beard, he may not even be any good - he's like Samson, his strength is in his (facial) hair.
The Yankees will now move on to other options, perhaps someone like Chris Perez, Jesse Crain, Edward Mujica, or Jose Veras.