They have an unsolvable conflict of interest. It is impossible for them to cure the conflict. If they attempt to do so, they will put an indelible stain on the courts that will cause great damage. She told the group that she favors homosexual marriage. And here we are in Massachusetts.
Nothing is easy.
It is a very subjective decision. When she gives money, she is putting her imprimatur on every organization which receives such money from her. She is telling the world and the judges beneath her that that organization represents the poor and the downtrodden. Every judge in the state is aware of the organizations which receive this benefit from their Chief. The Gay and Lesbian Advocates and Defenders receive money from her, and every judge in the state knows it.