What is the ruling on one who does not do something permissible in Islamic law to avoid embarrassment and judicial annulment under man-made laws? And does the ruling differ based on the country? And is he obligated to emigrate because of this?

There is no harm in abandoning permissible acts according to Islamic law if they are prohibited by man-made law, in order to avoid worldly punishment. This is not a matter of prohibiting what is lawful. It is stipulated that one must believe in its permissibility according to Islamic law. This falls under the category of warding off tribulation and harm from oneself, based on the Prophet's (PBUH) saying: "It is not fitting for a believer to humiliate himself" and "There should be neither harming nor reciprocating harm." This ruling does not differ from one country to another and does not necessitate emigration.