As I understand it, natural law theory argues that things in the world have a telos, and that the fulfillment of this telos is good. This metaphysical theory comes into conflict with many modern-day liberal ideas, such as the permissibility of abortion and the morality of sexual orientation.
If a thing belongs to a natural kind, it does so because it exemplifies certain properties - essential properties. It is essential that a proton be positively charged - if it were not positively charged, it would not be a proton.
What also seems apparent is that the greater in complexity we go (by complexity I mean the web of relations between the parts of the whole), the looser and looser natural kinds seem to become. Since there are more parts, and thus more relations, in the whole, many parts can be lost, even parts that may seem essential, while the overall integrity of the whole remains. Instead of identity being composed of static properties, these higher-level things are given their identity by what they are able to do.
In regards to sexual ethics, natural law theorists tends to look down on relationships that are not heterosexual. These relationships are not "natural" - they are "defective" in the same way a sociopath or a psychopath are "defective".
However, this analysis is flawed due to what was previously shown about higher-level entities. For example, the element Carbon has three isotopes - all of these carbons have essential properties, but they also act in their own unique ways. And as we go up in complexity, we also see far more variation. So a homosexual human is not "defective" just as an isotope of carbon is not "defective". The homosexual human is a tongue-in-cheek isotope of the human species. We use the term "defective" to describe a thing that is not doing what it ought to do, and in the scale of humans, what we ought to do has more to do with the social sphere than the personal sphere. Additionally, we might even be able to get away with calling a society an object of some sorts, with the goal of society being to provide a fertile ground for its inhabitants.
Some natural law theorists claim that the parts of a specimen have a telos themselves. A penis, for example, is meant for heterosexual reproduction, just as an eye is meant for sight. However, this analysis falls apart once again once we realize that a homosexual human being is like an isotope of the human species. We can show this further by appealing to the various vestigial organs of "more-evolved" organisms. For the amphibian who has moved onto land but retains its gills, the gills are not being used. In other cases, these vestigial organs end up evolving into newer functions - fins of fish may have evolved into arms, arms into wings. And so for the homosexual man, the penis serves a different role - the vestigial function is to aid in procreation, the new function is to derive pleasure or to simply pee.
For natural law theorists, the fulfilled telos is the goal - for Aristotle it was eudaimonia for humans, for Augustine it was union with God. However, even if we agree that the telos is the goal, we don't need to agree on the process we take to achieve this goal. There need not be a strict pattern for fulfilling the telos. It's also troubling that these theorists believe in a kind of ethical paternalism - they know what is good for you. When we go to a doctor, we expect them to tell us what is good for us. But what is good for us is good in a certain context: that of the continuation of life. Whereas these theorists believe they can identity what is good for us on the metaphysical scale.
Thus many natural law theorists end up proclaiming that the human telos is only achievable when the telos of all of its parts are working together like a well-oiled machine. Any happiness a gay couple has is "unnatural" or "unorthodox". But just as we would classify an oddly-behaving atom an isotope of its element, we can classify homosexuals as an biological "isotope" of the human species.
Furthermore, for someone who believes that composition just is identity like myself, natural kinds are merely handy concepts meant to group similar items together. Similar people can procreate and form a society not because they belong to a natural kind but because they are similar-enough that this is able to occur (re: ligers).