Like Mill, Stephen was a utilitarian. Like Mill, he was a liberal. Unlike Mill, he was what would have been at the time a more typical representative of both. It can be difficult for modern philosophers to put themselves back into that frame of reference, but it really is quite important for understanding both. Mill's On Liberty may be a standard text of what we call classical liberalism, but many liberals in his day considered it to be a dubious contribution to liberalism. And the reverse is also true; James Stephen often gets branded as a conservative, but he was a reformer and liberal through and through -- he just thought that Mill's version of liberalism was incoherent and that it cut off too many of the means by which genuine reforms could be furthered. This is precisely what Liberty, Equality, and Fraternity is: an argument that a coherent liberalism involves the use of means that Mill's ideas ruled out of court. In particular, he argues that genuine reform requires the use of government force in the interests of morality and religion, and that it is not only undesirable but impossible to regulate a nation and maintain it on a path of progress entirely by free discussion, with coercion only being used to stop or remedy definite cases of harm.
One of the things that Stephen considers problematic about Mill's account is that his restriction of coercion (not just government coercion but also the coercion of public opinion) amounts to an insistence that certain kinds of passions -- like fears -- should not be part of one's system of governance. This would have been very high on Stephen's list of concerns; when he wrote Liberty, Equality, and Fraternity, he was traveling back from India, where he had been on the Colonial Council and had been working on drafting laws to reduce the power of the caste system -- for instance, he was responsible for new rules of evidence according to which there was only one standard of evidence for everyone, regardless of caste or religion. While Mill very carefully formulates his harm principle so that it does not directly interfere with colonial policies (a fact usually overlooked in discussions of On Liberty), people like Stephen did not see themselves as doing in India anything other than the same kind of thing that utilitarian and liberal reformers were doing in Britain itself -- they were just at a different stage of progress. Stephen considers Mill's restriction of compulsion to be both detrimental to progress and inconsistent with human nature. Human beings, when deeply interested, as in cases of morality or religion, are drawn to the insistence that everybody should be on board with whatever moral or religious principle they are deeply interested in; it is not possible, in the statistical main, to have a society in which this has no effect whatsoever. This is not purely restricted to moral and religious matters, although those are the ones with which Stephen is primarily concerned; Stephen notes the acrimony that builds up in fairly abstract disputes and takes it to be the sign of an obvious fact, that we are not, and are not capable of being, purely neutral, however much we might try to hide it. Feelings occupy a great deal of our decisions and reasoning.
It is when considering this aspect in the context of religion that Stephen makes the remarks James quotes:
What do you think of yourself? What do you think of the world?...These are questions with which all must deal as it seems good to them. They are riddles of the Sphinx, and in some way or other we must deal with them. . . . In all important transactions of life we have to take a leap in the dark....If we decide to leave the riddles unanswered, that is a choice; if we waver in our answer, that, too, is a choice: but whatever choice we make, we make it at our peril. If a man chooses to turn his back altogether on God and the future, no one can prevent him; no one can show beyond reasonable doubt that he is mistaken. If a man thinks otherwise and acts as he thinks, I do not see that any one can prove that he is mistaken. Each must act as he thinks best; and if he is wrong, so much the worse for him. We stand on a mountain pass in the midst of whirling snow and blinding mist through which we get glimpses now and then of paths which may be deceptive. If we stand still we shall be frozen to death. If we take the wrong road we shall be dashed to pieces. We do not certainly know whether there is any right one. What must we do? ' Be strong and of a good courage.' Act for the best, hope for the best, and take what comes....If death ends all, we cannot meet death better.
James, of course, is not committed to Stephen's broader ethical and political views, just as Stephen is not committed to James's own ideas. There are certainly aspects of thought that James shares more with Mill than Stephen. But it's impossible not to recognize that Stephen's attack on Millian liberalism has broad resemblances to James's attack on Cliffordian ethics of belief. They both deny that the matters in question -- politics in the case of Stephen, inquiry in the case of James -- can be purely abstract; they both insist that the passions play an important and ineliminable role in guidance of their respective fields of discussion, and in some ways the important role; they are both insisting on what today would be called naturalizing the fields in question -- they are taking some normative principle held by their respective proponents on purely abstract principles and insisting on subordinating it to psychological facts; they both insist on the importance of action to our beliefs.