Bauer‘s got it right:

On the question of judicial candidates endorsing or campaigning with other nonjudicial candidates, Judge Berzon’s takes the problem to be one independent branch becoming beholden to or politically entangled with others, not corrupt relationships between the individual judge and supporters.  The worry is about a judiciary weakened in performing its critical “checking” function.  Berzon writes that when judges swap endorsements with legislative or executive candidates, or make speeches during nonjudicial political campaigns,” they build political alliances with allies and earn the enmities who don’t attract their support.

To take this theory seriously does not require subscribing to the fiction that judicial candidates are not politicians.  It better captures the reasons why they cannot be politicians in alliance with others who seeks offices in the other branches.