Do I need to render a salute to an officer when my hands are occupied?

While you were technically not wrong in being corrected, the second part of the reg stats “if not practical….” I would very often tell young soldier that I saw coming struggling with this same scenario not to worry, I appreciated the consideration, but would prefer they maintain their military bearing.

To me the effort to try to do the right thing was enough. What bothered me more was the total lack of discipline from the very new soldiers when I was around tradoc that bothered me more. And the complacency the Nico core had towards it.

Keep trying to do the right thing, if possible to render customs, do so. Hopefully you have good leadership in your units that see your dilemma and can do something similar to my COA.

No

The answer if you can render a hand salute. You simply acknowledge the officer and say at your liesure Sir or Maam.

You have a binder in one hand and a coffee cup in the other. Move them both to the same hand, cradling the binder in your elbow. Then salute. How difficult is that to figure out?

If you SHOULD be carrying a beverage, use a tumbler with a top to avoid spillage. Tuck binder under left arm and salute. Pull out handkerchief you carry for first aid purposes and offer to CSM silently (No, don't do this last one, really).

There is literal interpretation, and there is intent. For example, the intent of that guidance was for someone carrying awkward, or heavy, or two-handed objects. Someone who carries around a coffee cup and a binder, in my opinion, is trying to stretch that interpretation to avoid saluting. I'm sure things are much less stringent these days, but if it is reasonable to transfer objects to your left hand for the purpose of rendering a salute, then you are expected to do so. That is what the CSM is looking at. However, there are a lot of officers (above 2LT anyway) who are equally annoyed with saluting during day-to-day activities. I'm just saying, especially if the CSM is there, I wouldn't push it with this weak example of "hands full".

As long as you acknowledge them with the greeting of the day and Sir or Ma’am any Officer should be ok with that. Maybe a simple apology for not being able to salute if you feel the need.
Know the regulation quote it respectfully and fully.
Any Officer or NCO who honestly has issue with that has their own issues.

Call an Uber. Stay inside until your Uber arrives and make a run for it as the Captain and the CSM approach. Lie and tell them the Colonel needs his coffee and his binder as your Uber speeds away.

Another way of handling this situation is switch shirts with someone before you go outside. That way the name on your shirt gets the reprimand while you go free.

You salute is always the right answer

No you don't have to salute give the CPT a greeting and continue on your way if the CSM is not happy with that go to JAG and fight any type of UCMJ action.