I agree that historically, at least, respect has played a very important role in productive discourse.
I am not sure to what extent it is necessary in the digital domain--people are still people, of course, and thus will presumably want to receive discourse that is respectful (or at least not obviously disrespectful), but this could also be accomplished by elevating rare respectful speech--roughly the opposite of what happens now, where the outrageous is elevated because it drives engagement.
On the other hand, being respectful is not the same as believing what someone says. Humans have a variety of well-known cognitive biases (and some not-so-well-known ones), to the point that in certain ways we should expect most people to be wrong most of the time. It is hardly a virtue to rejoice in all varieties of wrongness in the guise of respect.
So we need two pieces: to seek reliability in our knowledge, and to do so with sufficient grace so that we can bring each other along.
I cannot with confidence ascertain how to accomplish this. If I had, I would already be working on it.