These folks were confused. They kept getting membership applications from priests, monks, and nuns, who kept going on and on about how good and righteous they were. But the members of the club were looking for idealist philosophers who were committed to philosophical holism, not a bunch of do-gooders.
Then they realized—oh, these folks think they want them to be "holy" as in pious. Nopers. This club is "holy" as in subscribing to the holistic view that all knowledge is a unity. And "idealist" here refers to someone who sees the mind as primary in determining what reality is like.
President and Founder
A lot of people miss Aristotle's holism. They see that he divides human knowledge into many different branches and sub-branches and then assume that he must think there is no unity to it. Wrong! All knowledge is ultimately of a single piece for the A-ster. There may be different areas of inquiry, but the notion of explanation works the same way in all of them, and all can therefore be expressed in terms of his formal logic.
As for his idealism—no, he is not like Plato in imagining a separate realm of ideas, distinct from the world around us (he's committed to holism, remember?). But for him, there is no fundamental distinction between how the mind structures reality and the structure of reality itself. That makes him a philosophical idealist.
Hegel put the "i" in "idealist" and the "h" in "holism." In fact, he's so much of an idealist he is an absolute idealist. And he's so much of a holist that he thinks every aspect of reality is fully expressed in terms of his philosophical system.
Okay, so the guy is crazy. And incomprehensible. But he does think that there is an identity between thought and being and that all of that thought/reality is a single whole. So he gets to be vice-president.
Resident 20th-century Guy
Few people would object to calling Quine a holist, especially since that's what he called himself. His whole approach is based on the idea that all knowledge forms a single, interconnected "web of beliefs," in which there are no essential divisions (even between logic or pure mathematics and the empirical sciences).
But Quine is an idealist?! He insists that he is a physicalist—that only material things exist! How dare you?
Calm down, calm down. It is true that he discards the notion of the mind in the traditional sense of the term. But language ends up playing pretty much the same role for him. In fact, his view (at bottom) is that we can make no sense of "reality" completely apart from the various linguistic systems we use to describe it.
Let him in the club!