The hat is just part of a uniform. A person wearing a hat with a crummy looking uniform is just as bad as the guy not wearing a hat with a great looking uniform who is being rude to customers. Both are extreamly unprofessional.
I don't wear a hat simply because it is one more thing to carry around, loose, and get dirty. I don't feel it makes me anymore or less professional. Like I said before, the hat at my company is optional.
Now for a person who's company requires the wear of a hat but he/she chooses not to wear it. That in my book makes them less professional because it show a lack of respect for the rules. I know some will say it is a miner infraction but what is the saying, "in for a penny, in for a pound." Meaning if you are willing to break that rule, what other rules are you willing to break. Also, when is it time to replace the hat? I see guys walking around with hats on that look just as old as they are. Is that a professional image? I almost feel like I am back in the military with the hat police.
You know some might say wearing a short sleeve shirt is unprofessional when compared to long sleeve shirts. When did short sleeves become ok?
Who is the benchmark as to how we should look, act, and perform?
Professionalism is not easy to define. In the civillian world, you must be your own policer of professionalism. The company you work for most likely does not do uniform inspections to police all of the crap people have on. Now compare that to a very professional group of people. The US Military, they clearly and strickly defined the standards of your appearance, they inspect your apperance for compliance, they police themselves (meaning your buddy will tell you that you look like SHT BAG and you need to fix it), and biggest thing is they have concequences for not following the rules.
I guess I could have just said that if you need the hat to feel professional by all means wear it.