If you are a multi-national with a legal presence in that country you likely have the resources to engage local counsel in answering that question and to assist in understanding the legal risks of various business decisions.
I don't ask for legal advice, I ask you how do you imagine the "always remove illegal content, easy" part of your plan to work? There's no common definition of what is legal. E.g do you suggest removing content if it's illegal anywhere in the world?
This really isn't a difficult question to answer: You remove the smallest subset of content such that you are allowed to operate in the markets in which you plan to operate/have a business presence in/plan to visit.
That's an imaginary simplicity since there is no such thing: determining a subset requires very high certainty in the rules (to be able to apply them and not run afoul), which doesn't exist in any real legal system
The defendant in question is a French citizen, being arrested in France, so if I were similarly situated I would expect to follow French law at a minimum.
My answer wasn't intended to be dismissive, truly, the answer will be specific to ones legal situation and the jurisdictions they plan to operate in and are best answered specifically by competent counsel in those jurisdictions after considering ones specific facts. Asking if ones should comply with laws "anywhere in the world" is not a useful question by itself.
Why would you not ask for legal advice on potential legal issues when registering users from countries you do not operate in? That is the only way you can understand the definitions of what is and is not legal in those countries.
I've never ran a web service personally, but to me it seems blocking access from UK, FR, DE is going to be the real long-term solution. Direct user participation from those regions are irrelevant anyway. That's going to narrow the problems down into actually working with police agencies in good faith and bypassing payment processors moral policing.
