Funny how when the Church focussed more on abortion and gay marriage that the GOP loved the pope but now that Francis has focussed on the environment and poverty that the lovefest is over.
I guess you weren't paying attention during the Iraq War debate? Did the Church's position on poverty change dramatically recently? Neither party is a Catholic party.
The view of conservative Catholics has been that outlined by Pope Benedict (then head of the CDF)
here. It has been usually been the case that the political issues where the GOP is closer to Catholic social teaching tend to be those where (1) there is no intrinsic evil and/or (2) the parties are not starkly at odds. The Church does not teach that immigration restriction, war, capital punishment, poverty, carbon emission, etc., are intrinsic evils like abortion. As a result, there is an acceptable diversity of views about how to deal with those issues.
On a different note, it is too bad that there is not more in the encyclical about the role of meat production and consumption in climate change.