What exact due process are we looking for here? If I donate to an extremist organization, and my boss finds out, is he required to still continue to employ me? Or can my boss only fire me if a government takes me to court?

Is my boss allowed to fire me because my job performance is poor? Or does he have to wait till the government puts me in jail for being a shitty sys admin?

I do find this idea that speech doesn't carry consequences really foreign and odd.