I agree. But in this example the SPLC is assuming the role of thought police.You have racial views that are non-mainstream.
You do not share them with anyone at work. At work, you perform very well. Nobody ever has a complaint.
But, the Southern Poverty Law Center discovers your identity. They call your boss and announce that you are a "white supremacist."
You are fired on the spot.
Is this right?
Depends entirely on what you do..and if you let it affect your work.
It's a tough call.
If you have a "public facing" and you are engaging in after hours racism by going to protests or associating with groups..it's very difficult to keep that "private" and does an effect.
However..if you work for the Department of Sanitation, picking up trash..you have very little public facing..and as long as you keep it off the job..and don't do anything illegal..there should be no problem.