When Bernard Margolis lost his job as president of the Boston Public Library in a power play with Mayor Menino, Bostonians called foul. It looked as if Our Popular Mayor was trying to politicize the BPL, a treasured -- and independent -- Boston institution. Now, amid revelations that three BPL trustees had undisclosed financial dealings with City Hall, the front-runner for the position appears to be former state Senate president Thomas F. Birmingham. The only problem? He has no library experience. The search committee for the position has also shortlisted five token professional librarians who are not friends with Menino.