"Rationalism" is an unfortunately overloaded term. In mainstream analytical history of philosophy, it is often used as a contrast class to "empiricism." "Rationalists" believe that "pure reason" gives us the best guide to truth, while "empiricists" favor experience. In this usage, Plato, Descartes, Spinoza, and Leibniz are "rationalists," while Hobbes, Locke, Berkeley, and Hume are characterized as "empiricists." While we do not object to this use of "rationalism," it has nothing to do with what we wish to address in this work.
Instead, the notion of "rationalism" we are dealing with is about the relationship of the abstract and the concrete. The common thread connecting our critics of rationalism is that each of them, in one way or another, criticized "abstract thought" not in and of itself, but insofar as it tried to replace "concrete thought," or tradition, or evolved moral rules, as a guide to how people actually should behave, or how they actually should evaluate certain proposals. (One thing that differentiates these thinkers is what exactly they contrast rationalism to.)
So, as a preliminary effort at clarifying what "rationalism" means, let us describe how we understand the "rationalism" that each of our thinkers criticizes, if not explicitly, then at least implicitly.
For Oakeshott, rationalism is first and foremost the attempt to dispense with practical know-how by substituting for it an abstraction drawn from practice. Such an attempt has no possibility of success, but it can nevertheless have pernicious consequences for those who try to pursue this "ideal." He sees rationalism as having an especially strong hold on politics, as the practitioners may not directly suffer the consequences of their faulty decision making themselves, but can impose those effects on others.
Hayek developed his critique of rationalism in the context of defeasing the socialist planner's pretense that he could "rationally" direct the entirety of a society's economic activity according to a plan worked out from purely theoretical knowledge of that society: no knowledge of "the circumstances of time and place" was necessary, according to the socialist planner. Unlike Oakeshott, Hayek tended to see the complement of rationalism as nonrational, rather than as a different form of reason from abstract thought.
Polanyi did not employ the term "rationalism," instead drawing a distinction between knowledge that can be explicitly stated, and "tacit knowledge," or knowing how to do something, perhaps without being able to state in rules or abstract principles exactly what one knows.
Again, Voegelin does not use the term "rationalism" in the way that Oakeshott and Hayek do, and instead attacks "ideology." While there is some difference in meaning here, there is also common ground: to Oakeshott, "rationalism in politics" presents itself as ideologies. And Voegelin understands ideologies to be destructive, for one reason, because they denigrate "common sense" and pragmatism, so that we would sensibly see Oakeshott and Voegelin both as advocates of "practical politics" as opposed to ideological politics.
Wittgenstein's main rationalist target was the attempt to turn thought, and in particular philosophical thought, into pure formalism. He noted that, for instance, our ability to follow a rule cannot have a merely formal foundation, but rests in a way of life that gives meaning to the formal specification.
MacIntyre's chief rationalist target is Enlightenment, or "encyclopedic," morality, which claims that it can work out moral behavior from abstract principles, without an "irrational" relaince on moral customs and habits.