The comments on the previous post have made me realize something that I've been chewing over for a while. If there's one single issue that really strikes at the core of the rationalist/non-rationalist divide, it's yeridas hadoros.
The notion of yeridas hadoros is rarely defined, but certainly most people take it mean that Rishonim, and all the more so Chazal, were more intelligent than us. With this understanding, yeridas hadoros conflicts with two aspects of rationalism.
One, which is more the Rishonic aspect of rationalism, is that rationalism maintains that there is a basically constant order of nature over history. Mankind doesn't change in its level of intelligence. Menachem Kellner, in his book Maimonides on the Decline of Generations, uses this argument and others to show that Rambam did not subscribe to the notion of yeridas hadoros.
The second way in which yeridas hadoros conflicts with rationalism is that rationalism mandates that claims require evidence proportionate to the degree that they are far-fetched. Until a few centuries ago, all mankind believed that the ancients were more intelligent than us. That's why it was virtually unthinkable to dispute Aristotle. Today, outside of traditionalists, people do not accept that the ancients were more intelligent than us. There is no evidence for it, a lot of evidence against it, and understandable reasons as to why people used to believe it to be the case.
Within the Torah world, aside from Rambam, it's hard to find those that oppose this understanding of yeridas hadoros. There is a discussion by R. Shlomo Fisher that approaches it, based on Kesef Mishnah, which I discussed in Sacred Monsters. Also, as noted, I heard a prominent Rosh Yeshivah from YU say, "Who says there's such a thing as yeridas hadoros?" But, understandably, this is something that most people would be wary of voicing their opinion on - it is dangerous in many ways.
There are many people who are rationalist vis-a-vis evolution, or Chazal's knowledge of science, but whose views on yeridas hadoros mean that they cannot be considered as full-blooded rationalists. (Of course, my own views on certain topics would probably also disqualify me from being considered a full-blooded rationalist by others.)