Blackboard with "You're fired!" written on it.
With the new administration in Washington, it may be time for a kinder, gentler approach to employee rights, but let’s not lose sight of the employer’s right to fire employees for misconduct, on and off the job.
If your employees were documented illegally storming the Capitol on January 6, you can fire them—as long as you fire everyone else who is documented engaging in illegal activity. 
Texas-based Goosehead Insurance did exactly that when they fired one of their attorneys who was responsible for Human Resources. Navistar reportedly fired an employee who wore his work badge into the Capitol.
Can you fire employees for their opinions? What if they stood outside the Capitol and yelled their support for the insurrection? People have a Constitutional right to express their opinions, no matter how odious. Does that mean a private company can’t fire them? 
Some of the people outside (and inside) wore sweatshirts that said “6MNE” which is reported to mean that the deaths of six million Jews were not enough. Yes, you read that right. Another was seen wearing a “Camp Auschwitz” shirt. Such despicable comments can and should be prohibited at work. If a Jewish co-worker of one of these people saw a picture of them wearing such a shirt, could they claim it creates a hostile environment to have to work near or with a person who clearly wants them dead? 
Typically, the courts have held that the outside behavior must affect the workplace in order for there to be a hostile environment. The cases usually involve a particular person being harassed by another. In this scenario, we’re assuming the Nazi doesn’t say anything at work. He just shows up. 
Let’s say Jewish employees say they feel uncomfortable working with the person, but it doesn’t meet the legal definition of a hostile environment. If the employer fired the Nazi employee, could he sue for wrongful termination? The short answer is “it depends.” Many states prohibit firing for political or otherwise legal activities outside of work, including California, Colorado, Illinois, Minnesota, Missouri, Montana, Nevada, New Mexico, New York, North Dakota, and Wisconsin. But is there a difference between political activity and hate speech? Arguably wearing these shirts is hate speech.
These state laws generally allow an employer to fire an at-will employee if keeping them on would hurt the employer’s business. If your employees say they’re uncomfortable, I would argue that it is affecting your business and justifies firing the person. 
What this means to you: If you don’t terminate these people, at the very least you need to watch them carefully for biased words and actions. If they are making decisions as managers about promotions and hiring, you need to be doubly vigilant. As always, seek advice from your attorneys before firing anyone.

Updated 02-08-2021

Information here is correct at the time it is posted. Case decisions cited here may be reversed. Please do not rely on this information without consulting an attorney first.