Where Mr Perriello writes that he doesn't want priests "driven by doctrine", if we take him seriously and the words seriously, that means that he would prefer that priests not be driven by the teachings of the Church, which are the Christian faith.

That clarifies the worth of the rest.

Regardless, why have nonChristian priests for a Christian laity? Why should any boy consider a vocation to a non-Christian/post-Christian priesthood?  Why should the laity put money in the basket every Sunday to give such men (and as Perriello would have it, women, but if we're not going to be Christian and the "priesthood" under discussion has nothing to do with Holy Orders, that's OK) in such a priesthood a livelihood.  And and why would non-Christians want priests at all?

If you want social justice, do it yourself.  As the Protestants would say, you don't need a mediator.  And per that there are already "women in ministry".  You don't have to be a priest in order to minister.  Try it sometime.