Religion is not politics. Religion is not philosophy.
There is no constitutional ban on the state having a political preference. There is no constitutional ban on the state having a philosophical preference. There is a constitutional ban on the state having a religious preference. If you can't distinguish between those, that is your issue. Most of us can, and the courts don't seem to have had any problem with it either.
Actually, I've done neither, your strawmen notwithstanding.
There is no constitutional ban on the state having a political preference. There is no constitutional ban on the state having a philosophical preference.
Is that so? So they can deny positions, promotions, and benefits - by law - based on the subject's political and philosophical views? That's the first I've heard of this.
Can you tell me in your own words what the reason for the establishment clause was? Because understanding that is essential to understanding its meaning.