Aveirah, you’d be surprised about how well informed R’ Bender is about these things. I think you’d also be surprised if you walked into the RIETS Beis Medrash on any evening during the zman.
As for the left-wing people who call themselves MO, you’re mistaken. They usually follow Avi Weiss, who doesn’t call himself MO, he used the term Open. Even the ones who don’t only make up a tiny part of the MO community. Just like in any community you have outliers, so too MO does. No MO Rav will back them, so they certainly don’t represent a valid view of Modern Orthodoxy.
You mentioned the case of the ex-teacher in Brooklyn. He doesn’t even claim to be MO, he and his family claim to be Chabad. He also claims to halachically be a woman, based on the psak of the Tzitz Eliezer, who ruled that if someone has the surgery, they are halachically the gender they currently have the parts of. While most disagree with this psak, the Tzitz Eliezer certainly was a gadol that may be relied on. My only question is did this person ask his own Rav and receive this psak (based on the T”E), or did he choose on his own to follow it?