I think your disagreement mainly stems from using different terminology: naturalgradient uses "left" as in "socially left/socially progressive", while you use "left" as in "economically left/socialism".
Plausible. On either choice, is the NYT a far left paper?
Btw, I don't think the accusation of its political leaning holds water, in saying plausible I mean I think you're right that the other person believes social justice headlines indicate left wing when to me, they just indicate normal middle of the road democrat positions.