"Police chief fired for calling "Black Lives Matter" a terrorist group on Facebook"
This is of course a lie, the chief left his post voluntarily, after acknowledging his mistake.
From your linked article:
“Bergman also said the chief is apologetic for how his statements have been interpreted, and that he removed the post on his own accord.”
It's perfectly appropriate for a jurisdiction to ask a chief of police to retire or otherwise leave his post once the chief has been demonstrated to be a liar, in this case propagating the lie that Black Lives Matter is a 'terrorist group'; public servants with such ignorance and hate cannot be trusted to serve the people in good faith, particularly those with the authority to arrest and detain.