No, they 'don't just go nuts'. They act in a way that seems to them to be rational when put against a narrative that they have come to believe. In fact the more rational they are the worse it becomes and the more completely they become deranged trying to fix reality to fit the narrative. I have had experience of a few people who navigate life by telling lies. The more effective liars construct a self consistent narrative for their lies. In the end they do go nuts, they come to believe that their counterfactual narrative is the actual truth - their rationality survives but reality goes.
If you study the history of revolutionary movements, both right and left, the playbook is the same. First you develop a narrative that feeds the discontent of a significant demographic in the population. That narrative entails the core idea that the current order is corrupt and rigged against them. The corruption is proposed to systematic if you're a left wing revolutionary, and want to change the economic order, and conspiratorial if you're a right wing revolutionary and are trying to take control of the economic order. The corruption narrative explains to its followers why all legal recourse fails - it's not because of the facts, it's because the whole system is apparently rigged. The whole legal system has to be uprooted so that it never charges the one the narrative says are innocent and convicts ant opponents of the narrative, regardless of any factual evidence against them. This narrative will usually entail the demonisation of sections of the society outside the target demographic. Very often these sections are delineated by ethnic origin. These people are dehumanised and radical ways proposed to exclude them. They are made to be the target for hatred, strengthening the emotional strength of the narrative.
This playbook has been followed time and again in different societies, with the same disastrous results for those societies. If it happens in the USA, the disastrous results will be for the whole world, because of the pre-eminent position of the USA. Imagine what the run-up to an extreme right take-over of the USA would look like. You'd see a whole movement growing around a narrative that didn't fit with the facts, and that mismatch being explained by the corruption of the basic structures of society, the legal system, the media, the civil service and so on. You'd see a propaganda machine put in place promoting that narrative. You'd see promotion of a 'strong' leader, who was going to sort this all out. The program of the strong leader would include making radical changes to the justice system so that the program and its advocates could not be challenged in court. You'd see proposals to suspend the constitution where it blocked this program. You'd see a program to cast doubt on the integrity of the election process, so that election results can be dismissed or overturned when they go the wrong way. You'd see armed groups assembled in support of the takeover. That is what has happened in all of the collapses of democratic states into authoritarianship that we have seen. Sometimes the takeover itself occurs when this mobilised minority can win an election due to vagaries of the electoral system. Sometimes it happens with a coup. Either way, the end result is always calamitous.
Political scientists would call this phenomenon 'fascism' (after the prototype, Mussolini's Fascist movement) and it happens all too often. The symptoms of the infection are quite clear, and those that wish to avoid the deadly effects of the disease need to recognise those symptoms and take preventative measures. The sad fact is that even good people can get caught up in the disease, because it preys on basic human nature and corrupts it. It's the cancer of democracy, and you can't blame individual cells for becoming cancerous. So no blame on individuals, it just needs to be recognised.