If one has given up the Christian Faith, it matters not whether they call themselves Christian.  Atheism under the guise of Christianity is still Atheism. Thus they cannot qualify as "separated brethren." They can only qualify as "separated brethren" if they are, in fact, Christian. 

Look at the likes of Joe Biden or Nancy Pelosi--they call themselves Catholic, but in fact have little to nothing to do with actual Catholicism.  They are cultural Catholics, not actual Catholics. They may not be atheists, but they are no Catholics. Rosaries and other Catholic accidents don't make one a Catholic. Being Catholic has to do with what one professes, not whether they like statues or Rosaries, or devotions to the saints. When it comes to Protestants you can have the same phenomenon. In the Jewish community you have the same phenomenon. Jewish is a term that can refer to ethnicity or culture as much as someone's belief system.