When the critic has no delicacy, he judges without any distinction, and is only affected by the grosser and more palpable qualities of the object: The finer touches pass unnoticed and disregarded. Where he is not aided by practice, his verdict is attended with confusion and hesitation. Where no comparison has been employed, the most frivolous beauties, such as rather merit the name of defects., are the object of his admiration. Where he lies under the influence of prejudice, all his natural sentiments are perverted. Where good sense is wanting, he is not qualified to discern the beauties of design and reasoning, which are the highest and most excellent.
Good taste is not something we all have already; it must be developed. Further, taste covers a spectrum. In some cases a failure to appreciate something as beautiful will be a sign of defect in oneself; in other cases the old maxim of de gustibus non disputandum will apply:
The general principles of taste are uniform in human nature: where men vary in their judgments, some defect or perversion in the faculties may commonly be remarked; proceeding either from prejudice, from want of practice, or want of delicacy; and there is just reason for approving one taste, and condemning another. But where there is such a diversity in the internal frame or external situation as is entirely blameless on both sides, and leaves no room to give one the preference above the other; in that case a certain degree of diversity in judgment is unavoidable, and we seek in vain for a standard, by which we can reconcile the contrary sentiments.
Thus we should expect variations when it comes to questions of (say) which of a number of truly great poets is the greatest. One person may prefer Ovid, another Horace, and argument over who is better may not be resolvable. (As we might put it today, among novelists one person may prefer Austen, another Dickens; and there is room enough in matters of taste for people who are unreasonable enough to prefer Dickens over Austen.) It becomes more acute across very different genres and styles. One person may prefer comic works, another tragic works; one person may like lyrics and another epics; and so on down the line. Breadth of good taste requires a sympathetic participation in very diverse views.
As with beauty, so with goodness, with the exception that moral sentiments are in Hume's view capable of being much stronger and more stable than aesthetic sentiments, and therefore establish stronger and more stable judgments. (It isn't clear that this is universal, and probably is not; there are very stable aesthetic judgments, e.g., that Virgil is an excellent poet, and there are relatively weak moral judgments, e.g., the 'lesser morality' of etiquette and good manners. But Hume, at least, has a very strong view of the consistency of basic moral judgments across human nature.)
While I don't think Hume is right that all of morality boils down to moral taste, I do think he is right that moral taste is an important part of our moral lives, which is what I'll focus on here. Consider a moment all the possible good things you might do in the world. You might work to shelter the homeless, or to further medical research, or to tutor children, or to keep the parks clean, or any number of other things. There are so many you can't do them all; there is no universal duty to help at pet shelters, for instance. But these things are admirable, excellent, and honorable, each important in their own way. However, no one is going to feel with exactly the same force the importance of each of these things; some people will be more powerfully moved by the plight of the homeless, some by the plight of stray animals. This is a sort of moral taste, and it is a powerful motivator. Indeed, when people talk about finding their 'calling' or 'vocation', they are usually not talking about a calling or vocation at all; they are talking about finding something to their moral taste. But there is also good and bad moral taste, since the quality of moral taste can also be affected by lack of prudent discernment, poor sense of priorities, and distorting prejudices. What is universal is the responsibility to cultivate good moral taste. And just as people help cultivate their good aesthetic taste by developing communities, as wine-tasters band together, or Austen lovers form societies, so an important part of our moral life is forming communities based on moral taste, through which we can cultivate and improve our own moral taste: people doing things that are not obligatory but nonetheless good, because they love to do them. There is an art to the good life, and we are capable of making our lives morally beautiful as well as morally right.