At my first "real" job, almost all the people in my department wore caps almost all the time (along with shorts, sandals or sneakers, and logo T-shirts). It was practically part of the dress code. What was the job? Sports editing! We were never 'in the field' (those people wore business casual to games or interviews, as did our managers), so there wasn't an excuse. There was one other woman in my department, and she dressed in the same fashion as the majority of the guys (whereas I wore whatever I felt like on a given day, with the exception of shorts or spaghetti straps, which was my self-imposed dress code).
Men in other departments wore caps on occasion, but it wasn't common except if they were balding.
In other words, it wouldn't occur to me to be "offended" by this, though it might be odd depending on the exact work environment.