I do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies foreign and domestic; that I will bear true faith and allegiance to the same. That I will obey the orders of the President of the United States and the orders of the officers appointed over me, according to regulations and the Uniform Code of Military Justice. So help me God.
You also swear to defend the Constitution and part of that is the first amendment. Interesting, isn't it?
My take on the oath (16 years Air Force) is that it is easy enough to recite it all. Every bit of the oath is binding and punishable if I fail to perform... except the last part. There are no lightening bolts that strike, no judgment forever more. The last part is a guilt trap to act as a catch all. You see, the majority will falter if they attempt to circumvent the oath because they believe in some sort of deity. I do not - therefore saying the last part is meaningless whether I say it or not.
I do, however, say it all because the officer swearing me in is most likely a Christian who can cause waves. Others might disagree with my thought process, but I am not concerned. Either way I walk away with a smile on my face and they are none the wiser.
You could say Dog and say it was a Freudian slip if asked.