I’ve found that people who have trouble identifying Christian fundamentalism, usually have very little trouble identifying Muslim fundamentalism. This is quite fascinating, given that the two have so much in common. To paraphrase one definition, I find fundamentalism to be not enough “fun”, too much “damn”, and too much “mental”.
- Insistence on specific historic Christian creeds and beliefs as dogma. This virtually always includes Trinitarianism, and typically includes inerrancy of some form or other (including the view that Scripture is inerrant on matters concerning faith and morals, but not on some other matters).
“Fundamentalism developed out of nineteenth-century Anglo-American evangelicalism. It was a strange coalition of diverse evangelical groups who rallied against the common enemy of theological liberalism. In particular, they were unified in upholding the truth of scripture—which they conceived primarily in terms of factual reliability—against the theories of higher criticism.”, Harriet A. Harris, Fundamentalism and Evangelicals (Clarendon Press, 1998), 2
“They perceive their task as being to defend the faith by defending the authority of the Bible. While they vary somewhat in their notions of biblical truth and authority they are in more agreement than their sometimes acrimonious debates and schisms would suggest.”, Harriet A. Harris, Fundamentalism and Evangelicals (Clarendon Press, 1998), 20
“As heirs of the fundamentalist tradition they perpetuated the fundamentalist doctrine of an error-free Bible within mainstream evangelical thought, even while they modified that doctrine in various ways.”, Harriet A. Harris, Fundamentalism and Evangelicals (Clarendon Press, 1998), 3
- Anti-modernism (especially hostility to the Enlightenment), and a typical preference for pre-modern theology, culture, and values while opposing modern values such as liberalism, modern feminism and LGBTQ+ rights. This often expresses itself in opposition to various forms of pluralism, such as globalization and multi-culturalism (which in turn tracks reliably with opposition to immigration), and a preference for separatism.
“ a militant opposition to modernism , both theologically and culturally, is what distinguishes Protestant fundamentalism from its conservative Protestant cousins”, Peter C. Hill and William Paul Williamson, The Psychology of Religious Fundamentalism (Guilford Press, 2005), 1
“Separatism remains the central distinguishing feature of self-proclaimed fundamentalists in the United States.”, Harriet A. Harris, Fundamentalism and Evangelicals (Clarendon Press, 1998), 3
“Religious pluralism is an inescapable feature of modernity. It implies choice, inviting the suspicion that there may be more than one path to salvation (perhaps even a non-religious path). The surge of fundamentalist movements, or movements of religious revitalization, we are witnessing in many parts of the world is a response to globalization and, more specifically, to the crises for believers that inevitably follows the recognition that there are ways of living and believing other than those deemed to have been decreed by one’s own tradition’s version of the deity.”, Malise Ruthven, Fundamentalism: A Very Short Introduction (OUP Oxford, 2007), 23
- Strict sexual mores. This includes mores regarding pre-marital chastity, marital monogamy, and reproductive rights for women (which are typically opposed in various ways). This is seen in both Protestant and Catholic fundamentalism, the latter of course emerging from a religious organization which prioritizes the authority of a celibate male priesthood.
“Several recent studies suggest that sex—or more specifically, the control of female sexuality—looms large in the language employed by fundamentalists.”, Malise Ruthven, Fundamentalism: The Search For Meaning (OUP Oxford, 2005), 102
“Historically, Grisez is credited with having played an important role in persuading Pope Paul VI not to relax the church’s stance concerning the impermissibility of contraception; the church’s traditional teachings on the issue were reiterated in the 1968 encyclical Humanae Vitae. Grisez’s arguments from the late 1970s concerning papal infallibility have been described as providing a “rallying point for theological conservatives” and as having influenced the Vatican’s pronouncements concerning the exclusion of women from the priesthood, whereas Michael Northcott talks of “[p]apal reliance” on Grisez’s and Finnis’s work in the 1990s when formulating a human-centered account of basic goods in the context of the “non-human created order.” Richard McBrien, in turn, suggests in his comprehensive study guide to Catholicism that theorists such as Grisez and Finnis “strongly support the teaching of the hierarchical magisterium on sexual and medical issues.””, David A. J. Richards, Fundamentalism in American Religion and Law: Obama’s Challenge to Patriarchy’s Threat to Democracy (Cambridge University Press, 2010), 87
“But the account also preserves traditional Catholic teaching about the intrinsic wrongness of contraception, abortion, and all forms of nonprocreative sex (including gay and lesbian sex) because, on the view taken by the new natural lawyers, all such actions threaten life, because they either end a life (abortion) or impede bringing a life into being through procreative sex. Its form of norm-based fundamentalism claims to find, in philosophical arguments rooted in an interpretation of the philosophy of Thomas Aquinas, support for a certainty about traditional views of sexuality and gender that condemn the constitutional developments discussed in Chapter 1.”, David A. J. Richards, Fundamentalism in American Religion and Law: Obama’s Challenge to Patriarchy’s Threat to Democracy (Cambridge University Press, 2010), 190
“It is these assumptions that explain why fundamentalist thought has been so obsessed with preserving a reading of Genesis, which contains the Adam and Eve narrative, as science. It is a narrative very much read as rationalizing a male reactionary discourse, God the Father, as patriarch, setting the terms of both gender and sexuality (the serpent) in terms of quite rigid gender roles. Eve’s fault was, on this patriarchal view, trusting her own experience as opposed to the word of God the Father, reflecting a deep distrust among fundamentalists of experience, including moral experience.”, David A. J. Richards, Fundamentalism in American Religion and Law: Obama’s Challenge to Patriarchy’s Threat to Democracy (Cambridge University Press, 2010), 162
- A pre-modern hermeneutic, and opposition to modern critical methods (especially the historical critical method). This also includes opposition to any form of what is perceived as “rationalist” or non-supernatural interpretations.  Note that although fundamentalism typically features various forms of literalism, a universal strictly literalistic hermeneutic is rarely applied except among fringe fundamentalist groups (such as flat earthers). As James Barr put it, “Even if fundamentalists sometimes say that they take the Bible literally, the facts of fundamentalist interpretation show that this is not so”. However, fundamentalists almost invariably appeal to the “plain reading” or “plain meaning” of Scripture, which they believe is the most appropriate primary hermeneutic.
“Christian fundamentalism started as an intellectual crusade against the historical-critical method applied to the Bible, but our brief look at the complexities of biblical interpretation in premodern times shows that fundamentalists are not going back to a more authentic Christian way of reading the Bible.”, Torkel Brekke, Fundamentalism: Prophecy and Protest in an Age of Globalization (Cambridge University Press, 2011), 187
“In particular, they were unified in upholding the truth of scripture—which they conceived primarily in terms of factual reliability—against the theories of higher criticism.”, Harriet A. Harris, Fundamentalism and Evangelicals (Clarendon Press, 1998), 2
“They cast aspersions on the ‘assured results’ of higher criticism (Johnson n.d.: ii. 49; Anderson n.d.: ii. 70), as did later evangelicals who questioned the supposed objectivity of historical criticism (cf. Manley 1926: 20; Packer 1958a: 141).”, Harriet A. Harris, Fundamentalism and Evangelicals (Clarendon Press, 1998), 27
“Fundamentalists in general avoid addressing ambiguities of language by arguing that the plain meanings of scriptures are an integral part of their moralizing purpose.”, Malise Ruthven, Fundamentalism: The Search For Meaning (OUP Oxford, 2005), 62
“Textual anomalies are either denied, or subsumed into the hermeneutics of inerrancy, where the burden of proof is shifted from God to humanity. They can then be explained as errors of human understanding, rather than flaws in the text itself.”, Malise Ruthven, Fundamentalism: The Search For Meaning (OUP Oxford, 2005), 66
- Fundamentalism typically correlates with science skepticism and anti-science attitudes. This is commonly seen in evolution denialism (specifically the modern evolutionary synthesis, though many fundamentalists reject almost all forms of evolution), and anthropogenic global warming denialism. I’ve already posted on this before, so I’ll only add a couple of citations here. Thomists in particular tend to have a conflicted relationship with science, since they have to acknowledge its success while holding that in tension with pre-modern Thomistic science and theology. 
“For most of its history, science has counted on the support of the intellectual establishment while criticism of science has come mostly from religious fundamentalists and literary romantics.”, Chet Raymo, Skeptics And True Believers (Random House, 2012)
“These faith-science tensions grounded in the creation-evolution debate generate a general distrust of mainstream science: The elite, atheist scientists who accept evolution are the same ones promoting the issue of climate change. In the view of some, if they get the former so wrong, why should evangelicals trust them on the latter?”, Katharine K. Wilkinson, Between God & Green: How Evangelicals Are Cultivating a Middle Ground on Climate Change (Oxford University Press, 2012)
I agree. In fact non-fundamentalists are typically more likely to reject concordism.
 Such as the idea that Jesus walked on a sandbar (rather than miraculously walking on water), or that the flood was a natural event which God warned Noah about (rather than a miraculous event caused directly by God), or that the Red Sea crossing was a natural event at which Moses arrived as a result of good timing helped by God (rather than a miraculous event caused directly by God).
 Some Thomists are prepared to accept that Thomstic science is wrong, and try to retcon it as metaphysics instead, but this is a perilous path since they know that once it’s acknowledged that Aquinas could be wrong on science then it must be acknowledged he may have been wrong about other subjects, such as theology, and then the whole house of cards will come falling down. I find a lot of Thomists will acknowledge Aquinas could in theory have been wrong about anything, but in practice never actually identify him as wrong about anything, and always find reasons why he isn’t in error.