You might be surprised to learn you can be booted off a flight for your attire, hygiene or odor.
Not exactly true. There are by law protected groups that can’t be refused the service just because they belong to that group.
You make it sound like it’s some kind of Trump shirt that wasn’t intentionally offensive. If that shit was an image of some other douche, he would have also been asked to leave as well.
That reason can’t be discriminatory, even on its face. And in some cases, like under ADA in US or EAA in EU, the requirements are even stricter. But yes, if the reason provided is not discriminatory or etherwise regulated by law, then they can refuse the service. But they can’t refuse for “any reason”.