I thought the principle you and the other poster were arguing for, was to minimize conflict. In the case of "bro" the conflict arises from a feminist critique of the word's usage in the context of a male dominated industry. In the case of the menorah, the conflict arises from the political controversy of the state of Israel, and its relationship to the Jewish community[0]. I don't have a problem with pro-Feminist websites or anti-Feminist websites, I just think it's professional to avoid stirring up debate with terms or symbols that would likely offend people with a particular viewpoint.
Perhaps you think the feminist viewpoint in this case is objectively correct and therefore deserves more consideration. In that case I would counter that the pro-Palestinian viewpoint is objectively correct. But my original argument was neutral on this issue.
[0] A relationship usually asserted to exist by the supporters of Israel, as is the case here.
"Those who have reason will have to use it..."