An example of a character that is supposed to be respectable is Colonel Grangerford.
The Grangerfords are a supposedly respectable family and seem nice enough—except that they are in a feud to the death with the Shepherdson family.
COL. GRANGERFORD WAS a gentleman, you see. He was a gentleman all over; and so was his family. He was well born, as the saying is, and that's worth as much in a man as it is in a horse… (ch 18)
In addition to being highborn, they are normally good people. Yet for some reason they are feuding with the Shepherdsons and as a result have murdered many of that family and have lost many family members themselves. They are obsessed with death and pride.
Huck admires the Grangerfords until Buck is killed. At that point he can’t take it anymore, realizing that the family is not as great as he thought. Although they may be respectable, they also think nothing of shooting someone for no reason.
Twain clearly feels that being highborn and respectable is not enough to make you a good person. He has Huck see Buck’s death because he wants the reader—and Huck—to realize that being a gentleman is not enough. To be a good person you have to follow your own code, not just your family’s or society’s. This is the choice that Huck himself had to make in not turning Jim in. Huck followed his own conscience.