I would go with two philosophies which sound contradictory. The first is practice hot, compete cool and the second is to train for reality. The question really was answered by your instructor: this style is a "hard style" and experiential school. You will learn very quickly if you can train in a kilt, yourself.

I probably would not wear the kilt, for this I'd wear, I don't even know what they're called, I buy them at value village. They're the weight lifter showy things with velcro waist, and a heavy sweat shirt. (In the formal class, I wear a heavy gi.) The concept is to train in a more awkward setting than the anticipated challenge. At the same time, the second philophy comes in: if I'm training for self defence, how does my normal wear work in that situation. It's a very critical part of the preparation. So, once in a while, I'd wear the kilt but I already know the fighting attributes of the kilt from childhood.

I was judging "sparring" (full contact black belt isn't sparring anymore) and there was a competitor from this style who came to fight in his normal clothes. There was a formal protest over his (non-traditional) clothing but the official response over-ruled based on his instructor's confirmation that street clothes was their normal uniform. (I can't remember how well he did, at that level, all styles are basically the same.)