The last time there was a major schism the nations of the day were explicitly aligned with one side of the other of the schism and the states attempted to crush the other side of the schism by force. Part of the separation of church and state in modern nations is meant to prevent church issues from becoming state issues (see the recent mainstream schism in the Methodist chuch which was completely peaceful and over similar issues).
The last time there was a major schism the nations of the day were explicitly aligned with one side of the other of the schism and the states attempted to crush the other side of the schism by force. Part of the separation of church and state in modern nations is meant to prevent church issues from becoming state issues (see the recent mainstream schism in the Methodist chuch which was completely peaceful and over similar issues).