[officialtony]

I don't see a problem with the hat. It lets people know that you care enough about the rules to be certified by the state. American Legion IS OBR rules, but at least you know the umpire has some decent training at some point. In our area up here, most everybody who wears the NAVY blue OHSAA shirts will wear their OHSAA hats with them. Many of the guys who do summer ball do not own any color shirt BUT NAVY, so they wear them year round. And I have NEVER heard any association up here demand that their umpires NOT wear OHSAA clothing unless they are doing an OHSAA game.
I own several different color shirts and have a Black Hat and Black Ball Bags to go with the Black, White, or Cream shirts I wear. I think it looks more professional to wear that combo together.
I'm not sure what your observation about the photos is concerned with. If it is because it IS OHSAA, I am fine with that. I am disappointed in the shirt however.

Looked at the pictures again. The shirt COULD be Blue.

Red Socks!?!?!?!?!?!?!?!?!?