I attended the University of San Diego, which had a Navy/Marine Corps ROTC.
On the days that they wore their uniforms to class, I noticed that they all carried their backpacks by the top strap, or if they used a briefcase type bag, they carried it by the handle, rather than strapping it over their shoulder.
I’m not sure if it was a written reg, but I know that they were encouraged NOT to wear a backpack as designed when they were in uniforms.
[my college flame was in the ROTC unit, so heard about the other rules & regs they had to follow, so while I don’t know from personal experience, I’m hoping you’ll take my answer with a little more weight than just some schmo off the street ;)]