Can your command make you clean someone’s house?

First and foremost, A superior’s order is presumed to be lawful and is disobeyed at the subordinate’s peril. Always keep that in mind.

Can your command "force" you to go clean someone's house? probably not. I seriously doubt someone is going to haul you physically over to the house and handcuff a mop to you.

Will you get into 'trouble' for not doing it - likely (probably every crap job coming to the Rear D's desk goes your way or other imaginative stuff...)

Are you disobeying a lawful order (i.e., UCMJ Article 92 stuff)? Yes, if it was put that way (instead of "Hey, who wants to go to Snuffy's house and help a buddy out?!").

Will you get into 'legal trouble' for not doing it - probably, but it's a gray area. Gray area because the order is not illegal, immoral or unethical (the usual trifecta for disobeying an order).

When they offer NJP to you and you go to a Court Martial because you refuse it, you can discuss strategy with your defense counsel while in pre-trial confinement. He'll likely try to argue that there isn't a valid military purpose.

However, the prosecutor will likely argue that it does have one because it is part and parcel of "promote the morale, discipline, and usefulness of unit members and directly with the maintenance of good order in the armed forces". You can roll your dice if you feel so strongly about it.

Does the order seem unfair? Absolutely. So does, "Snuffy, you take your mask off first to see if the nerve agent has dissipated..."

This serves a couple of purposes.

1) It helps a fellow member of the platoon. Whether this is on base or off base, forming ranks and cleaning the shit up will keep that SM from getting into deeper shit with whatever level of powers that be for housing.....Base Housing or Landlord. Either way, it'll help that SM in the long run.
2) It will get Leadership to have eyes on the direct problem at hand. This will not only help higher level of leadership have eyes on the situation to help provide assistance to the SM, but it will also show Leadership that the SMs FLL has failed in their duties. In fact, this will show the Leadership where all the failures have taken place.

He's going to be gone in the field for what 2 weeks, maybe 3? From the sounds of it, this house has been in disarray for months.

It is not ethical or moral to volun-tell people to go clean a grown man and woman's house. And since even base housing is privatized, I'd say that at best it's getting chalk on their feet of the legal line. Essentially what they're doing is forcing soldiers to provide a free house cleaning service to this member who chose to live like a slob. Or if you want to view it another way, they're forcing the government to pay for a house cleaning service of a lazy SM.

The guy is only in the field, he's not deployed. The house can stay nasty, and his leadership with their new found knowledge of his living habits can take the appropriate action to fix this soldier upon return to garrison.

It would be a completely different story if the leadership had said: 'hey, this soldier's house is a shit-show, who wants to go help him out while he's gone?' That's an opportunity for people to "take care of their buddy" as others have suggested.