[@mdk]

The question of how do we decide what is moral without foundational truths (i.e. moral values inherent in nature because God put them there etc) is a problem for lots of ethicists. One solution that his been put forward is using coherence theory, essentially meaning that for something to be true/correct it must be internally consistent. When applied to morality/laws this means that though morality is relativistic and might differ from culture to culture, moral judgements can still be made about a country's morality/laws.

So going back to Fakensia and its death for homosexual laws, there are ways it could be argued that these laws are wrong even if we accept that morality is relativistic when taking into consideration the principles of coherence. Lets say that Fakensia follows a mono-theistic style religion from which its legal system is based and one of the principle commandments of said religion and thus one its principle laws is something akin to Thou Shalt Not Kill. The law that allows for the killing of homosexuals is not coherent with this broader cultural moral framework, and thus can be objected to on more than just a subjective basis. 

Alternatively we could take the position of moral subjectivists (morality is only decided at the personal rather than cultural level) or moral skeptivists (that morality does not exist/is unknowable) to contest the unjust law. The former through a position of individual liberty, the latter through some kind of 'might makes right' conception.