Donald Trump’s running mate Mike Pence describes himself as an “evangelical Catholic.” By which he means that he is a Catholic who attends an evangelical megachurch. There are quite a few of those, including another presidential candidate, Marco Rubio. (Megachurches don’t make such a big deal about “membership,” unlike other Protestant churches, so it would be easier to maintain both identities with the megachurch model.)
Catholic apologist George Weigel has called for an “evangelical Catholicism,” by which he means Catholics evangelizing non-Christians.
Political pundits are using the term to group together conservative Catholics who agree with evangelicals on moral and social issues.