Our problem is not so much what people believe as the intensity and fanaticism with which they believe it.
For example, support for some kind of Brexit is a tenable position. But is a no-deal Brexit really worth the damage to social cohesion, the economy, the constitution and the GFA? Surely, only a fanatic would think so. Equally, on the Remain side the fact that Brexit has a popular mandate must mitigate the vehemence of one's views - and yet in too many cases it does not. The upshot of such fanaticism on both sides is that a compromise position - a soft Brexit - has long ceased to be an option despite its potential popularity.
Which poses the question. Why has fanaticism increased so much about - remember - a matter that was a low priority (pdf) only four years ago?
A lot of cognitive biases are at work. One is a form of what Dan Ariely calls the Ikea effect (pdf). If something costs us a lot of time and effort we infer not that it's too much trouble, as economic rationality suggests, but that it must be even more valuable than we thought. The difficulty of achieving Brexit (or Remain) thus becomes a reason for valuing it more highly.
Another is asymmetric Bayesianism, our tendency to downplay dissonant evidence whilst overweighting that which supports our position. The upshot of this is that the more we learn about an issue the more polarized our attitudes become.
Relatedly, there's a backlash effect. If our opponents seem unreasonable and intransigent, we are apt to become so ourselves by disregarding any worthwhile points they make and asking: why should I be the one to compromise?
A further factor is a form of selection effect. Our mass media selects for the shrillest voices either by giving their readers what they want to see, or by chasing clickbait, or because producers think a shouting match is good TV or radio.
On top of this, however, Brexit has become a matter of identity. "Leaver" and "Remainer" no longer describe merely one's attitude to the EU, but a host of other attitudes, towards immigration, climate change, the death penalty and so on. And arguments about identity are often much more fraught than ones about mere money (though of course the distinction between material interests and identity is blurred).
The background against which all this is happening also matters - that of economic stagnation. Back in 2006 Ben Friedman showed that economic weakness led to a weakening of liberal-democratic values. One reason for this, I suspect, is that if the economic pie isn't growing then any disagreement becomes a zero-sum game: victory for me means defeat for you. This fosters a more conflictual culture even on issues that are not ostensibly about money. (This is why I have little time for many centrist MPs, who claim to value liberal democracy whilst paying no heed to the economic base that fosters such values).
All of this brings me to Paul Evans' point:
We no longer have an established understanding of what the pre-conditions for a good democracy are.
Such conditions, I suspect, are not merely institutions and laws. They also require the right character. A healthy democracy requires that we have the capacity for cool, rational(ish) deliberation. Among many other things this requires that we be able to stand back from our own views and to understand others': what Rorty called liberal irony (pdf) and what Smith called sympathy (pdf).
Such virtues are now scarce. One hope, however, might be that passions which are easily inflamed can sometimes just as easily die away. But this is only a hope.
Another thing: It would be a cliché to quote Yeats' line about the worst being full of passionate intensity. I mention this only to point out the distinction of his brother Jack: he became the first man from independent Ireland to win an Olympic medal - for the painting which illustrates this piece.
And another thing: if you think there's any irony in a Marxist pointing out the dangers of fanaticism, you perhaps know little about Marxism or the human condition.