> How could EU law apply to a US publication?
Via business partners, treaties, subsidiaries, sister companies, and the restriction on the freedoms of individuals from those countries.
> Would US law apply to EU publications?
Yes, in exactly the same way. Whether one has to worry about it relates to the dependence of the two countries on each other and their relative military might.
> Is a representative from the EU going to show up in New York and serve Forbes a summons? I am genuinely curious how a US publication with no legal domicile in the EU have any obligation to follow EU laws.
Each relevant body in each EU state can act independently,
and they would presumably serve them a warning in any European office first, but for a US only company they would likely employ a US legal firm to deliver the letter for them. However its unlikely to be a summons, more likely a request for information followed by the penalty that is going to be imposed - there will probably be some opportunity for mediation and it could be escalated to a court.
> If a California resident goes to an EU insurance website, will that EU company have to comply with California insurance advertising laws?
Depends on Californias laws, but presuming the site was intentionally serving Californians then yes, it should, and would, be at risk of penalties in California.
> I think that there is a lot of wishful thinking about GDPR and a lot of ignorance on how jurisdiction works, especially internationally.
Undoubtedly
> GDPR has no jurisdiction over companies without an EU domicile or physical presence. And EU citizens aren’t protected unless they are actually resident in the EU.
The bodies that enforce the GDPR can recover their penalties by engaging any of many different legal apparatus, where they deem it appropriate (which will be rarely, if ever, as they have to convince other internal organisations to back them). It is harder, but by no means impossible, to recover money from abroad or to stop money transacting with a foreign entity.
Anyone present in the EU is 'protected', residence is not required.
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Forbes media have offices in Paris, Milan, and London. They regulary engage in both high value financial transactions and on the ground reporting in the EU. If they were prevented from operating inside the EU it would cause them severe operational issues, and their place as an authority in Western media would disappear overnight.