Hats: The odd one out
I find it quite hard to believe that anyone in his/her right mind can actually go to the office wearing any of the things mentioned. I don't even consider jeans and T-shirts appropriate for the office. All of them are just "things" that I don't consider part of a decent work-related wardrobe.
I would never hire anyone who dares to go to the office wearing pijamas, no matter how great software engineer they could be. Did they actually take a shower before going to work, or jumped straight from their bed to the car and to the office? But ...
"Nothing looks more stupid than a hat." Ladies and gentlemen alike ... " <- Stupid?
Hats? I centainly believe you are wrong in that bit. There is absolutely anything wrong with wearing hats when you are matching them with the appropriate clothing. They are classic, elegant, which is something that seems to be missing from the rest of the "things" in the slideshow. Maybe the view of a hat is different in Europe than in the US.
I know the CEO of a successful startup who always wears a hat. The hat has become part of his personality, almost a signature item that you associate with him and his company. He is always impecable and sends an image of classic elegance to the startup world, which sometimes seems to be in need of such example.
And he is not the only one wearing hats. Others in this part of the world wear hats, too. Even I was wearing a navy blue hat yesterday to complement a navy blue dress and shoes.
What you wear and how you wear it makes a startement about your personality. What you wear mirrors such things as laziness, poor hygene, it tells if the person is careless, or goes into detail; etc.
Once, during an interview, the person interviewing me didn't miss opportunity to look at my shoes. Some years after that, I asked her about this. She said that a few things tell so much about the person as the shoes they are wearing. She paid special attention to the detail and would never tolerate anyone badly dressed at work.
In terms of what some people wear in their home-office, well, it's an office and the place where you work after all. You shouldn't be wearing your pijamas in your home-office either during your working hours.