Whether or not you are correct depends wholly on how it's applied. If they attempt to fine someone for a normal volume of speech amongst friends, you're correct and the fine can be challenged and struck down. Mere presence of a 'profane' word has, as you have rightly pointed out, already been deemed protected. HOWEVER, there is a difference between wearing a shirt with a curse on it, or speaking it in a normal conversation, and sitting in a public area screaming curses just to annoy people. The laws do look at intent... the shirt in your example was a protest of government actions which is VERY explicitly what the first amendment was intended to protect. But when the intent is simply to cause disturbance, they take a dimmer view of it, so to successfully challenge the fine you'd need to argue that you had a legitimate reason behind your actions.
As it has been pointed out, this law actually isn't criminalizing anything that wasn't already disallowed. Excessive and loud swearing in public is already considered to fall under public disturbance. It merely gives the police chief a quick and easy way to punish the instances that really don't warrant actually arresting and charging a person with a misdemeanor.