I dont think thats true all the time. as we have seen with Biden, If a dem president is a centrist or far right for a dem, it shifts the entire party and the judiciary rightward. These things have monentum.

So I'd say its not simply the "D" that matters in overton shift. It also sets the topics in the political conversation, and either strengthens the party for the next election or leaves it in shattered and misaligned, like we are now about the unpopular far right wing genocide being pushed by a democratic US presidential administration.