I listened to it (Headlines show 102), and what you are saying is false.
Despite David Lichtenstein’s efforts to mislead, distort, confuse, and obfuscate, and his notorious creative editing of his program to twist things the way he wants them to be (he is a Clinton supporter after all), Rav Mendel Shafran shlit”a, and Rav Hershel Schachter shlit”a came out against what you say they are okay with in the program. Re clips from other rabbonim, there is a Litvish blog that did a review and analysis of that episode years ago and debunked it thoroughly. If someone does a Google search for the title of its post on the topic (Headlines Radio Program Advocates and Spins for Lubavitch Acceptance, Rabbis Wary) they will find it easily.