Hakatan: there is a very famous picture of Rav Aharon and Rav Soloveitchik together at a Chinuch Atzmai dinner. I don’t know if I’m allowed to post the link, but someone who was at the event saw the way they interacted with each other and describes how, Rav Aharon and Rav Soloveitchik respected each other. Again, they most definitely disagreed, but they had much respect for one another.
Also, again, I really think many of these quotes are taken out of context or misinterpreted.
And as to the mixed events: Who is denying that they are done on purpose? For those who believe that it is ok, the events are absolutely fine. I don’t think you understand the nature of these events if you believe it is “pritzus”. And again, if one’s personal belief is that it is not permitted, they would never be forced to attend.
There is not, and never has been, a “gay tolerance club” at YU. There used to be a tolerance club that disbanded several years ago, and it is my understanding that this club was not CH”V supporting arayos, but rather trying to help those who do suffer from such challenges (something along the lines of “hate the sin, not the sinner”). Either way, it does not exist any more after an event several years back had a lot of negative backlash, and to say it still exists or that it was in support of toeivah (which you didn’t say, just implied) is motzi sheim ra of a high degree.