The boycott of Columbia graduates by a group of judges led me to the following thoughts (adapted from a post about the 2022 boycott of Yale Law graduates, which was begun by a judge who is also one of the signatories to the Columbia boycott).
[A.] Just to make clear at the outset, I agree that judges are entitled to choose whom to hire, and that they indeed often prefer some law schools or colleges over others for many reasons that are often only weakly correlated to the school's relative academic quality. (Columbia students may well have been the beneficiary of such preferences far more often than they have been handicapped by such preferences.)
Indeed, I think that judges are even entitled, if they so choose, to hire clerks based in part on the clerks' ideological views, though I do not see the proposal as calling for that. Clerkships are the unusual sort of job for which ideological compatibility as to legal matters (e.g., originalism vs. living constitutionalism, textualism vs. purposivism, the interpretation of various controversial constitutional and statutory provisions, and the like) should generally be seen as a legitimate hiring criterion, cf. Elrod v. Burns and Branti v. Finkel. To my knowledge, many judges, both liberals and conservatives, have considered ideological compatibility in hiring clerks, though many others, both liberals and conservatives, have generally not considered it.