Skepticism, in which no premise or truth claim is regarded as above dispute (or, that it is always permissible and even praiseworthy to suspend one’s judgment on a matter), is the better comparison with rationalism-fundamentalism. It is interesting that skepticism today is often associated with agnostic or atheist religious beliefs, but I consider many religious thinkers in history to have been skeptics par excellence when judged by the standard of their own time. E.g. William Ockham (of Ockham’s razor) was a 14C Franciscan friar (and a fascinating figure) who denied papal infallibility. I count Martin Luther as belonging to the history of skepticism as well, for example, as well as much of the humanist movement that returned to the original Greek sources for the Bible, from the Latin Vulgate translation by Jerome.
The history of ideas is fun to read about. I am hardly an expert, but you may be interested by the history of Aristotelian rationalism, which gained prominence in the medieval west largely through the works of Averroes, a 12C Muslim philosopher who heavily favored Aristotle. In 13C, Thomas Aquinus wrote a definitive Catholic systematic theology, rejecting Averroes but embracing Aristotle. To this day, Catholic theology is still essentially Aristotelian.