Should know better.
You are absolutely correct about the public role of display team personnel. That Corporal needs to find another job.
I have related this story before as well but a few years ago I was showing some ATC cadets around our OCU building. One of the female cadets asked if girls could be fighter pilots. Before I could answer the (female) Flt Lt (VR) Officer with them said “of course not”. I told her she was wrong and she replied with “but it’s not encouraged is it?”. After I pointed out that she was again incorrect she acted like I had no idea what I was talking about. I quietly advised her male colleague to have a quiet word with her later.
BV