Let me offer the opinion from the other side of the fence: As an "instructor."
When I am standing in front of a class, you better believe I am in business casual. Typically, I will wear dress slacks and a polo shirt, or a dress shirt. No tie, because that is definitely too stuffy. I find that dressing like that, it signifies to the class that I take what I am doing seriously. It also hopefully signals to the class that I respect them; I feel that showing up in jeans and an untucked polo makes it look like I just happened to "stop by" the training center to facilitate the class.
It is proven that things like appearance (dress and hygiene) are big factors in communication.
It does bother me when pilots in the classes I facilitate show up in jeans, t-shirts, or gym shoes. It sends a signal to me that they don't really care about being in class today, nor do they take it seriously. More often than not, their actions and words during the class coincide with my preconceived notion based on their dress. The jeans and gym shoe crowd often is kicked back slouching in their chair, and either is falling asleep or quickly turning into the class clown. It is a broad generalization, but is true more often than not.
This is a career. Training is a major part of what we do as professionals, and it should be taken seriously. More and more, I'm seeing pilots who take their training less seriously, and I'm very afraid it is carrying over into how they operate out on the line. That might be why we see so many crazy variations of the pilot uniform these days.
Contrary to popular belief, training can be fun and relaxing even if you are taking it seriously. I have a lot of fun in the classes I facilitate, even with my dress slacks and dress shirt. Just like line operations, where I have fun and laugh a lot, even though I take my job seriously and do my best to fly the way I am supposed to do.
Just my humble opinion.