This is somewhat related to the recent inauguration but this practice has been going on for decades so I hope it's appropriate to ask here.

There's some interesting political discussion about this going on in the other thread, but someone suggested I also post here for a historical perspective. Below is my original post text:

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I know this isn't the first time it's happened but the specific references to "God" and "Jesus" by the preachers on stage just now got me thinking, isn't this is a blatant violation of our separation of church and state?

So I'm curious, why did this tradition begin and what is the rationale/historical context behind it? I found this Wikipedia article and this other article on the subject but they don't go into great detail about just why we do this (seems like it's mostly just an old tradition done for traditions sake?)