That said both east and west churches have sometimes honored bishops who were appointed by governments, or with questionable ordinations. It isn't a defacto defrocking on the basis of either though defrocking them is possible.
correct as usual. But just to clarify - the apostolic succession occurs with the ordination/consecration, not with the appointment. It's like the difference between being president and president-elect.
But never when the appointing government was made up of avowed atheists.