First, thank you for slogging through that article and taking the time to respond.
That rule from the Bible--not Liberalism--is a great way of formulating mutual respect as an ethic. Any way anyone gets to mutual respect as an ethic to govern one's actions is fine, but when it comes to governing the political process and the economy, basing that on a belief creates coercion.
Equality (not 'mutual respect') and liberty are the stated values of Liberalism. A requirement of mutual respect does follow from a belief in equality, but equality by itself is not a rule of any kind. Liberty is, by itself, the opposite of an ethic, i.e., a rule to constrain conduct.