In the workplace, we are used to parting with people whose job performance is unacceptable.
A more difficult question arises when someone has a viewpoint that is repugnant but who, to date, has not translated those thoughts into formal actions. For example, if an executive expresses a low opinion of employees in general, should upper management be compelled to wait until that opinion becomes a tangible, formal decision or is a pre-emptive strike permissible? What if the executive uses a racial slur, but the remark is behind closed doors and there is no evidence that the conduct has "gone public?" That latter, far more serious example takes us out of the realm of management and into illegal discrimination territory. It's an easier call.
We can argue, of course, that voicing an opinion is conduct. These are not unexpressed thoughts. Furthermore, the opinions are now on the record, so to speak, and could be cited as evidence of management indifference if the individual continues to misbehave.
The person's overall record should be considered and yet, in general, I find such individuals to be walking examples of the need for employment at will. I recall one executive who was as slippery as an eel in his ability to avoid a clear violation of company policy but who was widely felt - due his general demeanor - to be a complete bastard.
He would have been able to elude any attempt to pin down a specific violation. In his case, termination without cause would have more accurately been termination without specifically-describable cause. Either way, he had to go.