In the apple case you're referring to the government dropped its case after Apple argued that the government's demand constituted unconstitutional compelled speech.

In the united states the courts only have power at the pleasure of the constitution, the constitution is binding on all actions of a court. (Now, the courts could conclude some action doesn't violate the constitution-- but that's a different matter)

Except in some narrow cases in civil matters US courts do not order specific performance -- they don't order you to perform some specific act -- instead, the award cash damages for the harm you caused the other party.

In the ninth circuit where I reside, the standing, unchallenged, and unambiguous law that the publication of source code is speech protected by the first amending as was established in Bernstein v. US.

This is also recognized by the long line of modern decisions with respect to defamation law-- it cannot be so overpowered that it abridges the publics free speech rights, even though defamation is always a civil matter.

If you adopt an interpretation that the remedies available to the courts aren't constrained by the constitution, then any imaginable abrogation of the civil rights of the public could be lawfully imposed by simply creating a civil cause of action with the otherwise unconstitutional action as a remedy, then the state can induce some private actor to take action under the law. (The idea that Wright is acting on behalf of some state actor out to undermine Bitcoin is a common conspiracy theory, but a less parsimonious explanation than him being a simple con-artist.)

You're absolutely right that Wright's demand would also require that everyone adopt the alternative version and regard it as Bitcoin--- which is akin to expecting everyone to start believing he's a good guy, something no conceivable court could order because no court can never have power over the hearts of mankind (short of someone inventing a mind control gun :P ). It also has the practical problem that many of the defendants, such as myself, haven't been Bitcoin developers for years. And defendants, even the active ones, have no more ability to take action here that Wright himself does-- it's open source software, after all--, except for the fact that the defendants have a good reputation and Wright has a reputation as a fraud.

But to even get that far wright would also need to overcome the civil rights problems with his request-- at least for the US defendants: Wright is asking the government to compel labor to author the backdoored itself, compel speech by making the defendants publish it, and restrain their speech by prohibiting them from publishing non-backdoored code. He also would have to overcome the fact that the license they offered the software under expressly requires the recipient wave liability for any cause in connection with the software. (and the fact that his claimed loss is pretty obviously nonsense)

He also has to overcome a number of procedural issues, including the fact that the lawsuit was brought in the UK by an insolvent foreign shell corporation itself owned by a web of other insolvent shell companies in different jurisdictions -- none of whom operate in the UK against developers none of whom do business in the UK. Wright prefers the UK because of its motion-by-motion loser-pays default that lets Wright extract enormous legal fees by defeating summary judgement motions by offering forgeries (summary judgements are decided by assuming the facts are in the favor of the non-movant), as well as the weak protection for people's free speech rights. Wright's hail mary to try to keep in in the jurisdiction of the UK courts is to include one of his own entities as a defendant, and of course they immediately agreed to the jurisdiction.