I think if your supposed to be a professional then some sort of uniform is in order, just like any training, continuity is key.
The only thing I'd disagree with is the tie, it has no place in the cockpit.
But what is so badly wrong with shoes like DMs that do not mind oil and petrol, black trousers so your casual wear does not get ruined and a white shirt (or whatever top is appropriate to what climate your in) and during the winter the NATO pullover to help keep you warm.
Clothes may not matter for the quality of teaching, but bring a professional image and help with identifying your instructor(s)
Then again a PPL hired one of our A/C and turned up as mentioned with 4 gold bars draped on each shoulder. As I don't bother to wear them I felt very HUMBLE in his presence