Independent Judiciary means independent of the executive and legislative branches. It doesn't mean immunity to public rebuke. Plenty of judges have to renew their mandate by standing for election.

The incentives associated with having your career tied to elections can end up being suboptimal, so we could debate what the most effective method would be, but it's an example of how a judge can be removed from power by the public.

> Independent Judiciary means independent of the executive and legislative branches. It doesn't mean immunity to public rebuke.

This seems to be confirmed by the first sentence of the wikipedia article on "Judicial independence", but the second sentence also mentions not being subject to influence from "private or partisan interests".

>Plenty of judges have to renew their mandate by standing for election.

this is mostly a US thing, and only in certain states. Federal judges are appointed AFAIK.

Private means only for one person or group. It doesn't apply. And public rebuke doesn't imply partisanship.

Is the idea of an independent judiciary just a myth to manufacture consent?

It seems obvious to me that judges apply their own ideologies in their rulings. But IANAL, maybe I'm just too cynical.