In theory, the people we elect to represent us should. However, it turns out that people are pretty poor at picking candidates. As to it being a genuine problem with liberalism, yes, actually, that is it's biggest flaw, and it's why many groups who believe in the value of democracy are also often in opposition to liberalism, e.g. socialists. Liberalism tends to allow even the dreggest of dregs to have a bigger voice than they should.
But yes, the point is that, no matter how far you extend liberalism, at some point we all have beliefs that we believe are above debate. In cohesive societies, these beliefs run together more, and they contradict in other societies. Large cultural belief systems like these form the platform where debate is possible. In other words, if people diverge too far, no amount of debate can bring them together. And, again like Sartre said about antisemites, in many cases people aren't even looking for good faith debate.
In other words, I don't think many people believe you can convert the far right by debating them about race statistics. Politics simply doesn't work that way.
Politics can be based on compromise reached through debate. It seems history is quite an experiment in showing how often that isn't the case. In fact, most important political movements ever were not won through debates and compromise. Just look at the U.S.: ending slavery, civil rights, world wars, labor struggles, these all have a violent and serious past to them.
Ironically, the situation is not dire in the United States by external factors, but by domestic *******s who are willing to sacrifice the long-term health and stability of the country for short-term profit. As to our media, they're basically just capitalists, which means they push the stories not out of objective considerations for what's important, but for what gains viewers. Trump being outrageous garnered viewers. Capitalism worked directly against the good of the people in that instance.