Ok, yeah I have no idea and neither does anyone else here. You may get opinions sure, but not 100% "here's the right answer according to canon" because that doesn't exist.
In the real world (and I have no problem imagining this being the case in Battletech as well), it's very common for military cadet programs, whether that means military colleges/academies, as well as cadet corps within civilian universities, to have their own uniforms. It helps to distinguish the cadets from the actual serving military members. Alongside that, they'd have ribbons and medals and other things that are specific to that institution and being a cadet, that do not exist for FWLM members, and therefore their own protocol for how to wear them.
They may closely resemble the active duty military uniforms. I've seen programs that worked that way, particularly with field uniforms or the equivilant of battle dress uniforms. But have their own unique touches that indicates that person is a cadet. Yet other institutions may have uniforms (especially day-to-day uniforms and dress uniforms) that differ a LOT from its related real world military, giving their cadet corps a really unique look and appearance. Alongside that, they have their own book on how the uniform and any ribbons/medals should be worn.
Many cadet programs that have been around a long time also have longstanding traditions, often generations old, of how THEY do things, due to various traditions, that differ from how the active duty military does things.
I also don't have a hard time imagining that in Battletech, a cadet corps at a civilian university might have close ties to the planetary militia. They may even be considered a reserve component of that planetary militia. We've often seen planetary militia/defense forces that have their own uniforms and dress codes. In the real world I live in the USA, and there is a cadet corps at a university not far from where I live, and I know technically, they are actually considered a component of my state's national guard. In practical day-to-day terms it has little bearing on anything. It's practically fine print, it's easy to overlook. But in fact, that's the reality of their situation. Scale that up to the scale of a militia/defense force for an entire planet. It's not hard to imagine that being a thing.
All this to say.. I think you have maximum freedom to make this up. Whatever logic makes sense to you. As long as your player group and GM are ok with it, it works. I'm about 99% sure there is no canon answer for this.