Turning sick people away or making sick people leave would be impossible to enforce properly.
People vomit from motion sickness after rides. Food intolerances. GI issues. Medication. People have runny noses from allergies. People have chronic coughs due to asthma. Cystic Fibrosis. And soooo many more examples. They are in no way contagious.
I can’t believe anyone would actually want a theme park to have that much control and question individuals’ health based on the way they look or sound.