That is not my argument. I agree with you. If an asshole wants to wear a shirt with a word on that 99% of people in our society thinks is inappropriate, they have that right. You want to make an asshole of yourself by offending everyone with your free speech rights? Sure, go ahead, be that asshole.
No, my argument is that if I own a business, I have a right to refuse you service for any reason I see fit (except racial/gender/disability). If I, as a business owner, don't like people that wear purple shirts, I can ban purple shirt-wearers from my business. I can ban anyone that wears jean shorts.
And I can ban anyone that wears a shirt that has the word "fuck" on it.
Maybe you disagree with that right, but it is my right.
She wants to wear her "fuck" shirt? Fine, go ahead, be that douchebag and force kids all over the airport to read your ridiculous "look at me, I am actively trying to offend you!" fucking shirt. But the airline doesn't have to accommodate you.