You are not describing how democracies work. You're describing how we would both like them to work. You haven't yet given examples of major social change achieved through rational argument. You ignore the evidence that interracial marriage happened through the mechanism of bigots slowly dying off, not through rational argument. You ignore the example of slavery, the US's greatest perpetration of injustice. These problems were not sustained through reason alone, and neither were they solved that way.
> What you seem to be arguing for is that certain parties be shut out of the dialogue altogether, because their opinions deviate too far from those of your group
Mostly incorrect. It's not mainly about opinion for me; it's about behavior and intent. For example, the Westboro Baptist Church and the Aryan Brotherhood aren't writing carefully reasoned position papers. I'm ok with other people using their right of free speech to shout down their garbage. The problem is not their deviance from mainstream opinion, but the dangerousness of their propaganda and their drive to intimidate vulnerable groups. But if I discovered that a young cousin had come across some of their propaganda and wanted to talk it through, I'd be perfectly happy to do so, because it would be an actual discussion.
The problem you're not acknowledging is that speech has other purposes than carefully reasoned dialog. To the extent that people come open-minded to a topic and truly seek the truth, I think that's great. But that's a pretty small percentage of actual dialog.
I also think this objection is a little rich in that one of the major ways social injustice happens is by dominant groups suppressing minority voices. If you're all that concerned about people not being heard, it's not the voices of dominant groups that need such dogged protection from you.
> your opinion does not necessarily require rational underpinnings, so long as you feel certain enough of the righteousness of your cause.
Also mostly incorrect. I'd agree a bit in that our moral sense is prerational (see, e.g., deWaal's work on moral sense in animals), and values can't be established through pure reason. But I think it's important to have a reasoned understanding of those values and how to make them happen in the world. That said, I also don't think it's necessary to have a complete understanding before taking action; when someone is bleeding, the paramedics don't wait for the detectives to finish their work.
What I am saying (over and over) is that rational discussion is not enough to change unjust social structures. It would be nice, sure, but we are made out of meat, and we have to deal with our consequent lack of conformance to ideals.
I think you should also note the false objectivity in the "you seem" phrase. Unless you've shown what I wrote to a few thousand people and carefully measured responses, then I think you mean, "I interpret you as saying". That's not a minor nit here; a lot of the way social injustice happens is false conflation of personal or dominant-group views with objective truths.