I see a lot of people wearing jackets on the street with dojo affiliations blatantly displayed across their back. I don't think it's wrong to be proud of your training and I know the dojos appreciate the advertising, but for myself, it's not something i'd be wont to do.
I mean, truthfully, I'm not one to conceal my training and sometimes I think that I like to gab about martial arts a bit more than is necessary. That said, I can't help thinking in an anonymous situation like a city it might be like putting a target on your back for the macho drunk types who crave a pissing contest with someone "skilled" to prove their own worth. It could make someone increasingly defensive like many get when they see a police uniform. Also, any surprise you might create in a defensive situation--think pretending to be crazy or incompetent--could be eliminated as more caution may be taken in an assailants approach to you.
Perhaps it could help de-escalate a situation, I suppose, by making a potential attacker think twice. I dunno.
My Sensei says when he was on the competition circuit his club eventually wore gis without a crest so no one would no what style the fighters would be using. Likewise, a specific patch worn by an opponent indicating Tae Kwon Do or Goju could give him some insight into what to expect strategically.
Although the topic is likely no big deal, it was just bouncing around in my head.