cantoresq, I think you are convoluting respect and acceptance. Rav Schachter is respected by Chareidim (I’m not referring to every yodle who finds it necessary to give his two cents in a forum, but rather the Rabbinical establishment.) But his psak and opinions are not necessarily accepted.
When you say that “the left wing of Orthodoxy, is generally far more respectful of the right wing” you are actually alluding to acceptance more so than respect. Just on a basic level, what is there not to accept if someone is more stringent? (You can’t fault the next guy for having stringencies you don’t.) The reverse cannot necessarily be said. And indeed the left wing seeks advice from the Gedolim (who are on the right.)