The Church, as a whole, may be "walking the walk", but the US bishops dropped the ball a long time ago regarding immigration.  They rolled out the Justice for Immigrants Campaign, and, in many instances actually undermined the initiative.  this could have been a valuable tool for informing the people in the pews and initiating serious discussions about the issue of immigration.  Had the bishops done this, wee probably would have had Comprehensive Immigration Reform.  Instead, in many cases, the bishops chose to window dress.  In the diocese where I live, the campaign was headed by a nun who was proud of her lack of knowledge or understanding of immigration law.  The diocese gave her no support, and the committee sort of ran out of steam.  It's very likely this was replicated in other places.  It's clear that no informed conversation about this topic actually took place.