“”First, though, you must give to Caesar the law, then you may have Caesar give to God.””
If Cesar decides to make a state godless the Church usurps any law Caesar decides and ignores the state
From Pope Leo XIII
From Libertas
“Wherefore, civil society must acknowledge God as its Founder and Parent, and must obey and reverence His power and authority. Justice therefore forbids, and reason itself forbids, the State to be godless; or to adopt a line of action which would end in godlessness-namely, to treat the various religions (as they call them) alike, and to bestow upon them promiscuously equal rights and privileges. Since, then, the profession of one religion is necessary in the State, that religion must be professed which alone is true, and which can be recognized without difficulty, especially in Catholic States, because the marks of truth are, as it were, engraven upon it. This religion, therefore, the rulers of the State must preserve and protect, if they would provide-as they should do-with prudence and usefulness for the good of the community” (Leo XIII, Libertas, 21).
If Cesar decides to make a state godless the Church usurps any law Caesar decides and ignores the state
Where does it say that? The paragraph you posted listed the duties that the Church says that the State must do. It does not say what the Church or believers will do after a state has been made Godless.