The question is simple and direct here: what objective criteria are helpful* in admitting students to AP CS courses?
(By "helpful," I mean criteria that have some worth as indicator of future success in the course.)
Some context might help. Where I teach, there is no computer science pre-requisite to AP CS Principles, and when there was only AP CS A, there was not for that either. For most of my students, their first CS class is indeed an AP-level course.
Absent of this background, it is hard to predict what objective factors (I stress "objective" here for a reason) will help indicate how a student might perform at the AP level in CS. This is also crucial because all AP courses I've ever taken or taught have required applications due to both the rigorous nature of the course and the need to whittle down an applicant pool that is larger than the number of available spots in the course.
I have a couple theories of my own based on a few years of admitting students using several factors, but I will wait to self-answer until others share their practices.
Good answers need to include not only what the criteria used is, but also evidence - either in research or local practice - that supports the correlation between the chosen criteria and the eventual success, or lack thereof, of the students in AP CS courses (or, at a minimum reasonably advanced high school level CS courses).