Here is a business idea.
Someone sets up a company called Foreign Encryption Services (FES) in a foreign country like Russia, out of reach of the US courts. Anyone who wants to avoid turning their data over just needs to sign a license to FES that will exclusively and completely and irrevocably sell all of the content of their hard drives, clouds, phones, personal computers etc etc to FES. For $20 a month, FES will lease access to that content and the drives/cloud/phone etc back to you, encrypted. FES will provide you a key only if you certify that you are not facing any civil or criminal penalty. If you should be indicted, or sued, or compelled in any way by any court to turn over data, you are in violation of our agreement and FES will cease to provide you encryption keys and block your access to the data.
So even if the court compelled you, you couldn’t do it because 1) it isn’t yours (it belongs to FES) and 2) to give it would be to force a breach of contract with FES and 3) you don’t have they key to unlock it even if you did own it and didn’t face civil penalties for turning it over.
I sure don’t want to create ideas that will help criminals and pedophiles, and I understand the need for law and order, but in this day and age where data and ideas can be licensed, where stuff can be stored remotely and accessed remotely etc, the court is behind the times. This can be prevented by those who want to prevent it.
Something like that would probably be addressed via treaty. It might have to be in a truly enemy country (North Korea?) in which case you wouldn’t trust them with your data any further than you can throw them.
Better variation which would be more likely to pass legal tests: have your data on foreign server, and if you do not access the data for N days, it gets wiped. Then all you would have to do is stall for N days, and nobody but you knows what N is. Variation: have two pass phrases, where one shows your true data, and another shows innocuous data, and locks out or erases your true data.
In these days of multi-gig flash chips, you could also keep an encrypted copy of your data in a chip buried in the woods somewhere.