As Barry Loberfeld masterfully explains.
The way that liberals get away with pretending that they believe in "separation of church and state," as opposed to an atheocracy, is by defining atheism and secularism as inherently non-religious in nature and therefore immune to the First Amendment (e.g. it is perfectly acceptable for the state to annound atheism as the established church), or by defining "religion" so narrowly that "freedom of religion" is simply the freedom to claim a faith and to practice it in one's own head. The right to actually practice one's faith in one's life is dependent on its servility ot the values which the state wishes to impose.
So they pretend to believe in separation of church and state" while believing in big government, ultimately working toward the oppression and suppression of religion.
That is all.