Even as an open-minded person, it's likely that there are some issues where you're unpersuadable. For example, while I'm willing to listen to people explain why they're opposed to gay marriage, no matter what they say, my opinion that gay marriage should be legal isn't going to change. On the opposite extreme, undecided voters are persuadable because they haven't made up their minds. But, of the people who currently hold an opinion, some can be persuaded to change their minds, while others can't. Constructive discourse focuses on "persuadables" because they're genuinely willing to listen and they're willing to change their opinions.
If you found the speeches at the Republican National Convention unbearable, then it's likely that you're unpersuadable. The fact that you're upset doesn't matter because given finite resources, politicians only focus on votes that they think they can win.