I'm glad you asked that, I'm a vet and I've been wondering that for years. A couple years ago a retiree at the gym and I were on treadmills watching TV and even he asked me that question.
I'm anxious to hear the correct answer.......
Well I had 17 weeks of WW II infantry training and I don’t remember it being discussed. The command ‘sling arm’ meant muzzle up. As a practical matter I would not want a bayonet anywhere near my legs. Don’t recall it it was any different with the carbine but the M1 seemed more balanced muzzle up. Anyway rifle platoons only has M1. My platoon commander had a carbine. I have a picture of a Lt carrying a carbine after the war. Officers were armed, EM were not. If I find it I will let you know where he carried it. Actually it only mattered for parades. Otherwise you could do what you wanted for the best access.