The point comes up on a number of occasions in the book. It is perhaps put in the most straightforwardly striking form in the scene between Senator Bird and his wife Mary in chapter 9. When Senator Bird comes home one day, Mary Bird shows an unusual interest in his day, and it quickly comes out that she's interested because she has heard that the Senate has recently passed a fugitive slave bill. As she says, she thinks such a law would be "something downright cruel and unchristian." To her shock, she finds that her husband voted for it, and she scolds him for doing so, saying that it's a "shameful, wicked, abominable law" and that she'll break it if she ever gets a chance to do so. We then come to the following interesting exchange:
"But, Mary, just listen to me. Your feelings are all quite right, dear, and interesting, and I love you fro them; but, then, dear, we mustn't suffer our feelings to run away with our judgment; you must consider it's not a matter of private feeling,--there are great public interests invovled,--there is such a state of public agitation rising, that we must put aside our private feelings."
"Now, John, I don't know anything about politics, but I can read my Bible; and there I see that I must feed the hungry, clothe the naked, and comfort the desolate; and that Bible I mean to follow."
"But in cases where your doing so would involve a great public evil--"
"Obeying God never brings on public evils. I know it can't. It's always safest, all round, to do as He bids us."
"Now, listen to me, Mary, and I can state to you a very clear argument, to show--"
"O, nonsense, John! You can talk all night, but you wouldn't do it. I put it to you, John,--would you now turn away a poor, shivering, hungry creature from your door, because he was a runaway? Would you, now?"
This continues a bit, then ends in this way:
"Mary! Mary! My dear, let me reason with you."
"I hate reasoning, John,--especially reasoning on such subjects. There's a way you political folks have of coming round and round a plain right thing; and you don't believe in it yourselves, when it comes to practice. I know you well enough, John. You don't believe it's right any more than I do; and you wouldn't do it any sooner than I."
Mary, it seems, knows her husband well, because the senator goes on shortly afterward to break the law for which he had voted. The reason is clear:
Our good senator in his native state had not been exceeded by any of his brethren at Washington, in the sort of eloquence which has won for them immortal renown! How sublimely he had sat with his hands in his pockets, and scouted all sentimental weakness of those who would put the welfare of a few misrable fugitives before great state interests!
He was as bold as a lion about it, and "mightily convinced" not only himself, but everybody that heard him;--but then his idea of a fugitive was only an idea of the letters that spell the word,--or, at the most, the image of a little newspaper picture of a man with a stick and bundle, with "Ran away from the subscriber" under it. The magic of the real presence of distress,--the imploring human eye, the frail trembling human hand, the desparing appeal of helpless agony,--these he had never tried.
Face-to-face with reality, the reasoning, the 'extensive views', elaborate reasoning about the public interest, all fall away like the cobwebs they are, leaving the bare truth that the senator had known all along. As Mary had put it, all this senatorial deliberation, this bandying of arguments, was just a way of "coming round and round a plain right thing."
This question of when to stop balancing further arguments is an important ethical problem. Paradoxical as it may seem, there does appear to be a point after which further reasoning on a point is virtually bound to mire you in sophistries. However, we also clearly face the problem of distinguishing between accepting "a plain right thing" and straightforward irrational prejudice, and the line is much more difficult to draw clearly than one might think, because it is exactly the same problem as how to see clearly the "plain right thing", so that it brooks no further reasoning, without betraying reason in the process. That it can be done is seen in real-life cases that are similar to the fictional case of Senator and Mary Bird.
Stowe actually takes some trouble to deal with this problem. One part of her solution, as becomes very explicit in the last chapter, is for people to do more than denounce the evil of others: they must also look to the evil in themselves. This is reflected throughout the book. Stowe's novel is not a tirade against Southerners. As she notes, she was attempting to show Southerners not merely at the worst but also at their best, and in cases like the St. Clares she does a fair job of it. Further, she takes quite a few jabs, some blatantly sarcastic and some more subtle, at the racist prejudices found among Northerners -- indeed, even among Northern abolitionists, some of whom could talk benevolently and at great length of the slave's right to be treated as a human being as long as it were abstract, but who would shrink from being touched by a real slave.
A further part of her solution is sympathy. As she says in a striking passage toward the end of the novel:
But, what can any individual do? Of that, every individual can judge. There is one thing that every individual can do,--they can see to it that they feel right. An atmosphere of sympathetic influence encircles every human being; and the man or woman who feels strongly, healthily and justly, on the great interests of humanity, is a constant benefactor to the human race. See, then, to your sympathies in this matter! Are they in harmony with the sympathies of Christ? or ar ethey swayed and perverted by the sophistries of worldly policy?
Such a solution still leaves questions (e.g., about determining what is the "just" feeling). But it's clear that it goes some way toward dealing with the question. It requires self-critique and comparison of oneself with the moral ideal, explicitly and deliberately asking yourself whether you are being "swayed and perverted" by sophistries, and things like this.
And perhaps that's the best that could be said on this. But whether there's more to be said or not, this is a problem no one, whatever their walk of life, can reasonably choose to ignore.