Ty Cobb was a notoriously nasty individual. Would we have deprived him of a spot on the Detroit Tigers? Alexander Hamilton was notoriously unfaithful to his wife. Need I say more?
Being a jerk or unfaithful to your wife isn't illegal. Domestic abuse & assault is. So, is it right to fire someone accused of a crime? That's the question. I suppose it might depend on the nature of the crime, and whether it affects the merits of the job. ie: sexual abusers working with kids.