The increasingly bifurcated hiring process makes this less common now. Most of the liberal judges hire "on plan," meaning they wait to hire students at the end of their 2L year (they'll hire their 2024-25 class of clerks this June, for example). The conservative judges, by and large, do not follow the plan and hire much easier, midway through 1L in most cases. If you're a liberal interested in counter-clerking, most of the spots with conservatives are full by the time you're applying; if you're a conservative, it'd require passing up a lot of openings to wait for when the liberals start hiring.
Why so early: every judge, like every legal employer in America, is chasing after the same six people. There's only so many graduates of the elite law schools with perfect grades, and some judges care very much about whether they can send their clerks on to clerk at One First Street. Even if they don't, moving early lets you scoop the others and get the best talent available.
As to your first question: Is it really a surprise that the conservative judges tend to favor the scheme that maximizes their individual choice, while the liberal judges have by and large been more willing to go along with the centralized uniform plan? Liberal/conservative is, to be fair, pretty broad — plan compliance also varies a lot by circuit (eg DC is mostly on-plan, even the conservatives; the 10th is mostly off, even the liberals). But I think it makes a lot of sense.
