One thing that Morning Edition on NPR pointed out this morning is that that it's liberal, Democratic churches who have been pushing most strongly for the political activism parts of this... They want to be able to advocate for Democratic leaders in their community, and the local church is often the only consistent community organization in low-income black communities.
The Catholic vote generally tends to break down along the general electorate, at least, it has in the last ~8 presidential elections. Catholics are also less likely to be single issue voters than other Christian denominations, as Catholics make up a significant portion of North East Democrats and South West Latino Americans. Politically, economically, and culturally, Catholicism is a very diverse religion.