At what moment does the US military separate itself from the government when thinking the Soldiers creed and oath of enlistment ?

Yeah so I am confused a little by your comments: "Is there a moment where the US armed forces not partake in decisions made by congress when things get to political?". So it is not the Congress that gives you orders it is the civilian Secretary of Defense, usually at the behest of the President. So it is entirely the Executive Branch. Your scenario is also probably never going to happen. Why would I say that? The decision on if the order by Secretary of Defense was lawful or not would be made far above your level. Highly unlikely an NCO would make that call. Only time you would be concerned with a lawful or unlawful order is if your LT or CO decided to take matters into their own hands and issue their own special orders. Otherwise I do not see your scenario happening. Unless you can lay out the scenario in more detail in which I could be persuaded it might happen?

tough question to answer. Our first priority is the Constitution, our second priority is to obey the orders of the office of POTUS. Who ever holds the office. We have court systems, and laws, that will determine if, what the Person who is holding the office does with their executive orders, is constitutional or not. Just like the last idiot in the office, this idiot will try to make do on what he promised. There will be advocacy groups that will challenge his executive orders, and courts will determine. Keep in mind that individual states have the power to defy those executive orders to a degree, and even ignore certain laws put forth by Congress.

Case in point - Illegal immigrants or undocumented immigrants - depending upon which term you support.

I can not say at what moment this will come. But it will have to be clear cut violation of the constitution. Clear cut meaning they are going against the constitution by direct or indirect means (circumventing the constitution by laws or orders).
I am a conservative, a Veteran and an American that takes his OATH seriously. It has been said by several that the military will not go against the people and by some that it will follow orders(meaning they will go against the people). You will be either against the people or against the government if congress, the president and senate have their way.
I don't know about the rest of you brothers and this goes for all of you left leaners or conservatives because all of you are brothers. I think the time is coming you will have to make a decision. This decision will be either to fight the people or the government.
The way I see it at this point, there is only three ways this can go if the democratic controlled government continues their agenda.
1. A military coup. Which would save a lot of blood shed.
2. A civil war of which the USA would not survive for either side of the issues.
3. Continue letting it go and learn to be a socialist/communist.

Now for me when they take away my rights, I will start shooting anyone that comes to force me. I know I will die but dam it I will die free and trying to uphold the oath I took. I am to old to go and fight them at their places so all I can do is fight from here.
You brothers will have to make that same decision. You will not be able to sit on the fences as a lot of Americans will do. You best make up your minds before it happens, so you can be prepared.

There is reasons I wish, that if it comes to the constitution being clearly attacked that a coup would happen. First off a coup would not be an out and out war. Oh there may be some fighting against some of the more active organizations that is for socialism.
Among these reasons are that if civil war happened it would be more a gorilla warfare and the targets would be anything that would hurt the government control. These targets would include the electrical grids. A document posted by someone that was in the Department of Homeland Security has stated any 2 or 3 month time period of the electrical power grid failure would cause approximately 9 out of 10 Americans to die.
You people leaning left take this into consideration in making your decisions. Because most of the gun owning Americans, veterans and good old back country boys are not going to stand for a socialist government.
There is nothing else can be said about this. If the government changes or disobeys the constitution which we swore an oath to then it is up to you if America dies, lives free or is communist.
I can see no good outcome for any of us.

I think it's important to point out that the Congress doesn't issue orders to the military, the President of the United States is in fact the Commander in Chief and he directs the military via the Chain of Command. We are sworn to obey the (lawful) orders of the Commander in Chief and to protect the Constitution against all enemies foreign and domestic. I served under Presidents I despised - Clinton and Presidents I found to be the most honorable men in our history - Reagan. Regardless how I felt about them, I obeyed every legal order. If they had issued an illegal order I would not have obeyed. Period. Personally I believe Biden is incompetent to serve and his running mate is just as bad - I am thrilled that I am no longer on active duty but if I were I would hold my nose and still adhere to my oath. Regardless whether or not Biden is competent I reject the notion that he is trying to hurt the country - he simply doesn't have the cognitive skills to not screw up the job.

I think the separation was quite apparent yesterday when the Commander in Chief didn't remember the name of his appointee and the position of the Secretary of Defense. The separation was finalized when he couldn't remember the name of the building, you know, the Pentagon. "I want to thank Sec-, the former general, I keep calling him 'General.' My - the guy who runs that outfit over there," Biden said, before quickly adding, "I want to make sure we thank the secretary for all he's done." (Ibetson for Mainline, 9 March, 2021).

It's really going to be fun times if he decides to play around with the nuclear football and doesn't have any idea what it is. So yeah, as long as Biden's POTUS, don't worry about politics and the military. If Biden steps down, Harris will probably dismantle the military unless the payoffs from the military industry are substantial. BTW, the whole Biden not knowing his Sec Def, or being able to name the Pentagon is True, look it up.

My oath is to the constitution and not to the leaders I serve under.

There is NO moment that you describe. Decisions made by Congress, should they go "against the Constitution" will be ultimately decided on by the Supreme Court and/or the voting citizens of the US. The new "leadership" you seem to abhor will still be the Commander in Chief and our President. Your oath is not limited to obeying those officers and Presidents you like.

Look SSG (Join to see), it is, very simply put, The POTUS is the Commander in Chief of the United States Armed Forces and the Command Authority of the Country. As such, when we take an Oath to do our duties, to honor others and to respect our Country, we include in this framework the POTUS. Therefore, giving respect to Country is honoring your Commander in Chief in your commitment to your Oath. Biden or Trump; Clinton, Bush or Obama, the size and color is immaterial, because the Armed Forces in it's commitment to defend our Country is apolitical, yet it's orders are from the POTUS.

At this point, it seems clear that the answer is:
You are bound by your oath to obey all orders from the POTUS and the Chain of Command.
If it is an unlawful order, however, you are not bound.
The question might then be "What is an unlawful order?".
Most of us seem clear on the obvious stuff. LOAC rules provide guidance. Killing unarmed civilians is an obvious example. Implementing ordinary orders from "above" (using "quotes" to make the term more generic) is another obvious example.
I think the discussion might hinge on examples that are less than obvious. I am wondering if respondents could consider if this might be the crux of disagreement in this discussion. What do y'all think?

Never go against the people with political orders. Always follow Constitution. Meaning no confiscation orders like they did during hurricane Katrina where they had military confiscating firearms from law abiding citizens. Follow Constitution that is the first thing.