It’s very hard to see how this CAP inquiry can amount to anything. First of all, it seems very unlikely that Alito will have been much more than just a “member,” since if he was a major leader or donor or organizer or anything like that, wouldn’t he have mentioned that in his job application letter? And, if he did have more than a marginal involvement, then he would have remembered it–this guy is awfully smart, after all–and he knows it would be futile and dangerous to try to cover it up.
It also would make no sense to brag about his membership in CAP for reasons other than it being a respectable and conservative organization. For instance, you wouldn’t brag about being a member of the KKK. I was in the Reagan administration at the time (next door neighbor to Alito at the Justice Department, by the way), and it is absurd to think that anyone then thought that it would be a smart move to brag about belonging to a racist or sexist organization. To the contrary: It would have been a scandal for someone working on civil rights issues, in particular, to be revealed as having racist ties.
So the most that can be revealed is that there were some racists or sexists in CAP, and that there were some racist or sexist sentiments that appeared sometimes in its publication. But to tar Alito with his membership, you would have to prove at a minimum either (a) that he was so intimately involved with the organization that he must have known about these folks, or (b) that CAP was so well known as racist and sexist and that Alito must have known this even if he wasn’t a higher up. But “(a)” is belied by the first paragraph above, and “(b)” is refuted by the second paragraph above. Q.E.D.