I don't accept your definition of fundamentalism. Such movements are about some kind of return to fundamentals, correct ethics & behaviours (eg recovering modesty, rejecting 'foreign' practices), & uncompromising reforms/reformations.
Or your definition of irrational as opposed to reason. Love is irrational, unreasoned. But it is not opposed to reason, reasoning and rationality are just irrelevant to that mode of life, where our animal concerns and genes are the relevant way to engage, not our intellect.
I'd look at the way rightwing and conservative views, are linked to threat perception. People living near border conflicts, or experiencing a pandemic, tend to become more hostile to out-groups, and more intolerant of ambiguity.
Wahabism/Salafism, nicknamed 'Islamic puritanism', rose in popularity as the Islamic world experienced a reversal: the loss of the Mughal Empire to the British, the fall of the Ottoman Empire and carving up of the Middle East that led eventually to the creation of Israel. And in the 1970s when the school experienced it's most explosive growth, the imposition of the Shah in Iran against their democratic choice that led to the Iranian revolution and Iran becoming a religious-led state, the Soviet invasion of Afghanistan that led to the creation of the Taliban and Al Qaida, and the huge rise in oil prices following the oil crisees in '73 and '79 that threw a spotlight on Saudi Arabia and amped up Western shennanigans there, where Mecca is.
Robert Sapolsky draws attention to what we would now call OCD behaviours by Luther, in terms of understanding the role of these behaviours in human history, in creating rituals, and on religious governance, in ways that have powerful impacts on cohesion during times of crisis. So we see the rise of protestantism, with the 30 years war, the rising tensions that led to the Defenstration Of Prague, and the English Civil War. The English and Dutch rose from a low base economically and militarily, to dominate the Catholic empires of the Portugese and Spanish, attributed to the so-called 'Protestant work ethic', but more realistically attributable to stricter governance and more judgemental neighbours.
In the history of Judaism, there is a lot of fundamentalist-type behaviour, and OCD ritual. The carrying of the Ark of the Covenant in the desert. The instructions around entering the holy of holies in the temple. And dietary laws - there is a saying 'It's not that Jews keep the dietary laws, it's dietary laws that keep the Jews'.
Chinese rebel religious movements have many times had a zeal towards ethical reform that might be described as the Confucian culture equivalent of puritanism: Liu Bang & the success of the Confucian Han over the brutal Qin; the Yellow Turban, White Lotus & Boxer Rebellions; and the rise of Chinese communism - linked by historians to providing a kind of nationalism that the whole population could participate in. Government antipathy to the Falun Gong, & the Dalai Lama, have to be understood against this background.
Chaos, bad leadership and corruption, lead to reform movements, which often have a fanatical edge. Nationalism in the Weimar Republic, and India & the USA (see rise of conspiracy theories as reaction to loss of trust in regulation & government). The mafia as it started in Sicily, maybe the most invaded bit of the Mediterranean, began as a mode of belonging (rather than purely as a criminal enterprise) that could outlast waves of different rulers who only saw the people there as means to their ends. I link these types of trend to social contracts and game theory here: Is the tyrannicide perpetrated by William Tell morally legitimate?
So, fundamentalism can be intelligible, maybe even seem sensible as a reform movement with the socio-cultural means available. Is, or can it be, rational though? I say no, because these movements are driven by instinctive concerns, the game-theory violation of the social contract, that makes the current situation intolerable, to the point of widespread commitment to change things or die trying.
If you look at Durkheim's understanding of religion, as about social cohesion from the enactment by the community of shared attitudes to sacred things, then you have to recognise the commitment to habeus corpus in the UK, or free speech in the US, as literally sacred values - challenge the value, challenge the basis of cohesion of the community. Jonathan Haidt with his Moral Foundations theory, talks about different cultures having different moral palettes, sensitivity to different dynamics - ie those with purity/sanctity being far more present on the right, those with heightened threat-perception.
These moral-dynamic settings of a community are about game-theory dynamics, and relevant Bayesian priors not just in history but in a culture's narrative of itself (eg US military policy & budget is still living in the Cold War). We don't reason ourselves into our morality, there's no 'ought' from an 'is'. The flourishing of a community or not, is the only true arbiter for an ethical system.