@Nav And there's the key point: "as long as the employee is well behaved". If your free-time activities revolve around white supremacy, antisemitism, gay-bashing or anything like that, it's entirely reasonable for your employer to assume you don't leave those opinions at the door. That creates a real risk for other employees, and for the employer if/when anything happens relating to this.
@Nav If someone wanted to get a colleague fired and the colleague is carrying out racist activities in their free time, they could post things they know to be true about their colleague, and the company may pay attention. If the colleague isn't doing this, they can show that this is all faked-up nonsense, and of course they're not going to get fired.