Why should being pro-environment preclude being pro-life? Why can’t Republicans worry about economic inequality, and Democrats consider devolving more power to localities and states? Does opposing the Iraq war mean that you have to endorse an anything-goes approach to bioethics? Does supporting free trade require supporting the death penalty?In other words, the Pope is a bit of a compassionate conservative.
These questions, and many others like them, are the kind that a healthy political system would allow voters and politicians to explore.
To repeat an old, obvious, point, the central problem for compassionate conservatism is that in order to win it's got to appeal to minorities; however, minorities and white evangelicals don't like each other very much, and it's hard to find a politician that appeals to both groups. Bush tried to build a coalition that the Pope would presumably have approved of, but it collapsed disastrously with that immigration bill. This issue has remained vexed because of the increasing importance of the southwest, where social conservatives are rabidly anti-immigrant. (It should not be surprising, btw, that people who talk about "local communities" are usually racists.)
The current conservative coalition is sustained by a quid pro quo between social conservatives who don't care much about economics, and corporate interests that don't care much about social issues. (I guess there's also a primarily racist-nationalist wing, mostly white, male, and disgruntled.) All three of these groups are politically toxic, even -- to some extent -- to one another, which is why the Republicans are in deep political trouble. But it seems like even so they fit better together than they do with, e.g., minorities or union members.