There has been a separation of church and state since the constitution was written.
Feel free to lie. We've rejected theocracy by not allowing for religious tests to hold office. None of that puts a separation between church and state. The opposite. Pastor, ministers, priests, and nuns could all run for office. Lay people too. It wasn't about what you think it means. Not at all.
It's there for good reason. So we don't turn into a theocracy like Iran.
No, its there because it is a truly Christian notion of acceptance of others and to keep religious civil wars from consuming the country as it had the old world.
That said the people came for religious freedom and expected to have government reflect that and to include them in a meaningful way. They fully expected to participate in government and have their faith present in government. Christians have had their faith kicked out.
God has been declared unconstitutional by Democrats by force using their deviant liberals values to accomplish that feat.