I think the classic example is copyright and hacking offences, of which there are many many examples. Legal in a person's home country, very illegal in the US (unless you are a big corporation, of course).
Usually, countries only respect extradition treaties when there is an equivalent law on their books
(the workaround would be to charge someone with bullshit charges for the extradition)
The main issue is that few countries respect freedom of speech on principle and even that group has edge cases.
There is a grade to crimes. Lesser crimes are only punishable if they were done in a country. Bigger crimes are punishable even if you did them outside of the country.
Imagine that your own country finds out that you were a prolific serial killer while on a holiday in another country. Do you think they will just ignore it?
This is because your home country has jurisdiction over you and is more than free to write laws punishing you for whatever they want.
This is country B considering something a citizen of country A did while in country A to be a crime. And not that it even matters but in country A that thing is legal. Like country B is a sovereign state and can arrest you for whatever it wants while you're there but the bigger question is whether country A should be mad about it and impress themselves on country B to get them to not do that.
That's really the issue here and exactly what the GRANITE Act he's proposing does.
It seems like the US is actually being too nice here. It's a perfectly reasonable position to reject the notion that a country has global jurisdiction and to consider such an arrest to be a hostile act against the US. I would be pissed the moment a country thought it could punish one of my citizens for something they did while under my jurisdiction—even something that I consider to be illegal.
There are cases in which refugees were tried in the EU, when there was a suspicion that they committed war crimes in Syria while being citizens of the country.
Or imagine that country X with age of consent of 18 would find out that the citizen of country X while home, married 8yo child and impregnated her.
It's the same principle. So there is nothing special about extending jurisdiction beyond your own borders.
The issue in this case is that Freedom of Speech is such a fundamental right, that it should not be forbidden anywhere in the world. Sadly, it is forbidden in most Western countries, let alone developing.
The idea is that a website in the US can be accessed by UK users, no matter what blocks are put in place on either end. Agree that the US shouldn't be nice about this though.
Mens rea usually means intent to do the thing, not intent to commit a crime.
E.g. if I involuntarily swing my arm and hit someone in the face as a result of a medical condition I lacked the appropriate mens rea and am not guilty. If I intentionally punch someone in the face while being somehow unaware that I'm not allowed to do that I am guilty.
Hard to see how mens rea would save anyone from being guilty here.
Pretty much avoid entering Britain or its dependencies or you'll be nabbed on a Commonwealth Warrant and extradited to England.