They generally don't have to proactively police it, but they have to answer court orders in every country that has courts, or they'll be in trouble in that country. And countries are free to cooperate with each other to enforce these.

Pavel Durov was arrested when he traveled to France because Telegram was noncompliant with French court orders. You can ignore them in Russia... you can't ignore them in France. And you can ignore Russian court orders in France but not in Russia. And the Russian or Indian court is free to ask the Montenegrin government to suspend your domain name and the Montenegrin government is free to agree or disagree.