Mr. Underwood, who "despises Negroes...won't have one near him" (Ch. 16) does not necessarily believe in gratuitous cruelty to them or in breaking the law in order to do them harm.
Named after a Confederate general, Braxton Bragg, who was an advisor to Jefferson Davis, Mr. Underwood is a highly intelligent and educated man who runs the local newspaper office. As a legitimate and ethical journalist, Mr. Underwood surely knows the value of the rule of law. So, when he keeps an eye on Atticus Finch on the night that Atticus guards the door to the cell of Tom Robinson, Mr. Underwood anticipates a lynch mob and is determined that injustice not occur. From his open window, Mr. Underwood points his shotgun when a mob appears. After this mob departs, Braxton Underwood has a long talk with Atticus.
Further, after the travesty of a trial for Tom Robinson, Mr. Underwood writes a scathing editorial that is an invective against the injustice dealt by the jury.
Mr. Underwood simply figured it was a sin to kill cripples, be they standing, sitting, or escaping. He likened Tom's death to the senseless slaughter of songbirds by hunters and children.
He may "despise Negroes," but Mr. Underwood has ethics and he believes in justice.