Would you obey an illegal or unconstitutional order?

If an order is demonstrably illegal then every service member is honor bound to disobey it. If there is no way to determine legality one way or another then it's dealers choice. Just keep in mind that either way you will be held accountable for YOUR actions, most assuredly if you harm American Citizens based upon your choices. Where is "the line" when dealing with tyrannical political dictates and illegal actions (criminal) to maintain or usurp political authority? Read up on the Battle of Athens, 1946.

If I knew the order What is unlawful / Illegal And Dangerous to the common good I definitely would not obey it. I answer it that way because If my boss told me to go next-door and steal a I need pin from somebody else so we could get the job done I just might do it. But you're obviously talking aboutA real world situation todayAnd there is a real fearThat what you're talking about might happen. I believe / And hope That there are enough good people at the Pentagon in all the walls of the military That he just couldn't do this.

Wouldn't obey an illegal order or unlawful order but the US military isn't bound by the Constitution so the answer to that part of the question would obviously be yes. WDE!

No.

Seems to me that main stream media has been making this same spin since the election

The very minute he issues that order he will be a Enemy of the State and should be arrested on site secert service will have to stand down and president arrested vp assumes the presidency speaker of the house moves into the vice president seat until jan 20,2021

Our President Top Joint Cheifs
Should all be charged and removed. And if or when the president declares martial law
Every Branch Needs To Stand Down and Protect America
We all took that Oath and i will stand behind it until i die
I, (NAME), 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; and 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
Right now We Have A President
That had broken his oath and is on a fine line of an UNLAWFUL ORDER

It is incumbent upon the individual Soldier, Sailor, Marine, Airman, or officer to determine whether the order is illegal or unconstitutional (based on his own knowledge of applicable law and of the Constitution), and whether the order was morally right (for instance, if disobeying it would cause a non-negligible degree of harm relative to its benefits). So the short answer to the basic question is that it depends on the SM and on the order he's been given.

As to your "for instance," which is very specific (and partisan) to current U.S. politics, it is neither clear that such a scenario is or would be unconstitutional or illegal, because of the current issues regarding the election itself to-date. Furthermore, your WITF article is from June and has nothing whatever to do with your first example. Would it be illegal for the President, as CinC, to "deploy military to ... stop violent protests," as the headline says? It might be if it was federal troops. More likely would be a federalizing of the Guard to address the emergency, as Ike did when Democrats sought to forcefully prevent school integration in '57. They were STATE guardsmen, stood up in defiance of and opposition to their own STATE's governor.
Was Ike out of line?
Should the Guard told DC to pound sand?
Was following that order the right thing to do?

The regs say that "commissioned officers are obligated to follow lawful orders irrespective of their personal opinions on the matter." But the law itself is what he must apply to know if orders are lawful or not.

Nope

So will this order be labeled so?