Well, as one of your customers, may I put my two bobs worth in.
In my working environment, it is becoming less common to see people wearing ties. I am a consultant and most of my customers are moving towards polo shirts / open neck cotton shirts with the company logo and slacks. I tend to dress to match my customers and, even through winter, wear a company polo shirt. I consider myself a professional and do not feel that I am under dressed considering the climate here.
Given this, I would not expect to see my instructor appear with a tie on when it is 40 deg on the tarmac, and the cockpit is going to be a darned sight warmer. This is simply ludicrous. Our instructors all wear open necked cotton shirts and dark blue slacks. This is neat and IMO comfortable. I do not think less of their professionalism because they are not wearing a tie.