Before it was 'Hosen aus' for 'pants off.' Is 'ab' used for coats? Can both be used? Maybe 'aus' is used for pants because when you take them off you are sort of coming out of them and it isn't really seen the same way with coats. I'm just guessing of course.
"Hut ab, Mütze ab" short for "abnehmen", "Schuhe aus, Mantel aus, Hose aus ..." (or other clothes) short for "ausziehen". Any one of them is pretty impolite, maybe possible as an order for kids or soldiers, and I guess "coat off" is no better.
A civilized person would say "Nimmst du bitte die Mütze ab." "Nehmen Sie bitte den Hut ab" "Ziehen Sie bitte die Schuhe aus."
"Legen Sie bitte den Mantel ab." (Only for "Mantel", "Jacke" or "Anorak", maybe also for "Hut", because "ablegen" means to take off in a formal situation as when coming inside as a guest.) You could also say "Legen Sie bitte ab", generally meaning please take off your outdoor clothing. So I guess "Mantel ab" could have been meant (by duolingo) as short for "Mantel ablegen" but this is self contradictory, because you would never be impolite when using the polite "ablegen",