Why were they being turned away? Because they were wearing clothing which effectively stands as pro-Trump political speech.

"Listen, I am a Trump supporter. I'm doing my job, dude. You're on private property, you need to leave. You're acting like the far left."; -an as yet unnamed security guard making a cuttingly astute observation concerning the behavior of typical Trump-paraphernalia wearing Trump supporters (and apparently violating the 1st Amendment at Ron DeSantis direction) as they attempted to access a Florida Books-A-Million book signing event open to the public and chaired by -you guessed it- Ron DeSantis.