You are so very right, the very key, heart, and point of the matter is that it is personal, very personal. Why is it important to display personal beliefs in public gatherings? or submit others to your personal beliefs in a public forum? That is what churches, mosques, and temples are for, demonstrating and professing your personal beliefs in the appropriate forums. It is not usually atheists that stand up and for the Establishment Clause. It is generally those who hold profound spiritual beliefs that stand firm for the rights of all, any faith or belief, to attend and participate in government and public functions that are free from religious overtones, which are deeply personal spiritual convictions. These are not required to conduct or participate in public proceedings or events. It does not mean those that gather at secular functions are godless or atheistic, it is just not the appropriate place or time, and that is what the framers intended.
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