I am a right leaning American who subscribes to the New Yorker. I find a lot of their essays to be surprisingly non-partisan. I especially enjoy the fiction pieces.
Right-leaning Democrats definitely do though.
‘Right-leaning democrats?’ Right compared to who? Lenin?
Contrary to popular belief among Americans, the Democratic party is very clearly right-wing by global standards. There is a "progressive" fringe (with little institutional power) that basically wants what would elsewhere be centrist liberal policies, and an even fringier "leftist" wing (with zero institutional power) that wants the party to essentially be a euro-style Labor party.
American left is the global middle. The non U.S. right is the american left.
The U.S. Democratic Party is about as right-leaning as many mainstream right wing parties in Europe.