What do you do when a soldier refuses to listen to your directions?

We would have had a discussion he would not have liked

DA 670-, 3–10. Eyeglasses, sunglasses, and contact lenses. if this individual has refused refer to the aforementioned paragraph of 670-1. i would recommend corrective training prior to 4856, you don't want to appear impotent in front of your subordinates, this would allow you to have a teachable moment with this soldier and your formation. earn their respect, it doesn't automatically come with the stripes.

Charge him!

I'm not sure exactly why we are debating breaking their private property vs smoking the soldier and why we have young LT's summarily endorsing their negative behavior by saying it's their right to protect their private property. 26 years ago my GYSGT would have made me wish he had smashed my glasses now we have to ask the soldier if it's ok to correct them on their misgivings as we might hurt their feelings you. I didn't force you to sign the papers that said you will obey my lawful orders but I'm going to ensure you do.

My Dad would have pulled them off and stomped them. I shudder what he would do after the soldier made a move or mouthed off again.

Counseling statement

Find out the reasons why SM would not remove them. Regardless, unless it's medical based the SM was wrong. Paper work is a good thing to document but if this was out of character for this SM then find out, as a person, not an NCO, what's going on. Explain why, regulation out for reference. Wording on the 4856 is up to you within reason.

I'd imagine the culture of the unit would also be a deciding factor. I can see some groups needing to place a greater importance on immediately following orders, regardless of external factors, whereas others very much need to take those external factors into account and root them out before getting too harsh.
Creating a paper-trail early on in a soldier's career can be the wrong way to go about it.
Most important in any situation like this is to ask "Why?" rather than to just go off the chain and start yelling. A lot of times I see leadership assume the worst, only to have the situation be at least marginally understandable - the guy might still be jacked up, but it might be more a misunderstanding on his part and an opportunity for a "educational" experience.
For small issues - like refusing to remove sunglasses - you don't want to have something plague them later on. Once their fault is clear, take them aside and correct them as heavy-handedly as necessary. Before creating a paper-trail, determine if there are outside issues resulting in an abnormal behavior (home issues, financial, et cetera). Once you determine that they actually have a lasting behavioral problem, then start that paper-trail so that if it continues, you've started the process to prove they either need to have a more formal "correction" or expulsion.

I am not certain how this could even happen. Unless the individual has some kind of condition that REQUIRES protective eyewear, he has absolutely no leg to stand on. If the NCO in charge issues an order to remove the eyewear and the order is refused, he should dismiss the individual from the formation.
Then, after explaining the situation to the remainder of the formation, take the idiot directly to the side to have him explain why he is above the rules.
I can stomach all the talk about preserving individual rights, however, following orders is part of the job. If anyone serving in the armed forces places his "rights" to free speech or expression above the need for good order and discipline, that individual needs to go home. He will eventually get someone hurt.
There is absolutely no room for this type of insubordination. I'm not going to reminisce about the good old days when the offender would have been pounded into the ground by his platoon mates. Those days are over. But if you build the type of team that will follow your commands without question because they trust and respect you, you will never find yourself in this situation.
I would think that someone being so boldly defiant is the result of poor leadership at some level.
Root cause = he has no fear of repercussion. From the team, you or your boss. He should learn differently by experiencing the consequences of violating regulations. Do it right. Use your chain of command. That goes both directions.

Here is what the Army Regulation says:
IAW AR 670-1 PG 15 3–10. Eyeglasses, sunglasses, and contact lenses
Note: This paragraph is punitive with regard to Soldiers. Violation by Soldiers may result in adverse administrative action and/or charges under the provisions of the UCMJ.
a. Eyeglasses and sunglasses.
(1) Conservative civilian prescription eyeglasses are authorized for wear with all uniforms.
(2) Conservative prescription and nonprescription sunglasses are authorized for wear when in a garrison environment, except while indoors. Individuals who are required by medical authority to wear sunglasses for medical reasons, other than refractive error, may wear them, except when health or safety considerations apply. Commanders may authorize sunglasses in formations or field environments, as appropriate.
(3) Eyeglasses or sunglasses that are trendy or have lenses or frames with conspicuous initials, designs, or other adornments are not authorized for wear. Soldiers may not wear lenses with extreme or trendy colors, which include, but are not limited to, red, yellow, blue, purple, bright green, or orange. Lens colors must be traditional gray, brown, or dark green shades. Personnel will not wear lenses or frames that are so large or so small that they detract from the appearance of the uniform. Personnel will not attach chains or ribbons to eyeglasses. Eyeglass restraints (to include bands) are authorized when required for safety purposes. Personnel will not hang eyeglasses or eyeglass cases on the uniform and may not let glasses hang from eyeglass restraints down the front of the uniform. Glasses may not be worn on top of the head at any time.
(4) Soldiers are authorized to wear ballistic spectacle eye protection issued by the Army, including lens colors or logos that do not comply with paragraph 3–10a(3), above, in garrison or field environments unless otherwise directed by their chain of command. See the Army Combat Readiness Center for a list of currently approved protective eyewear.
b. Restrictions on contact lenses. Tinted or colored contact lenses are not authorized for wear with the uniform. The only exception is for opaque lenses that are prescribed medically for eye injuries. Clear lenses that have designs on them that change the contour of the iris are not authorized for wear with the uniform. Contact lenses may be restricted by the commander for safety or mission requirements.

Find out what the unit policy is about wearing sunglasses in formation, some units made it a requirement while downrange. Next if there isn't a policy talk to your PLT SGT and 1SG in that order and suggest that one needs to be drafted up and signed by the commander in order to maintain good order and discipline in the unit. If the Soldier has a medical reason then he needs to carry his profile to limit the amount of questions.
I hope this helps.