Although there is not consensus about what would make a natural kind natural, most traditional views agree that naturalness is a monadic feature; ie, "K is a natural kind" can be true or false of a given kind without specifying any further parameters. Call this the monadic presumption.
A few philosophers of science have denied this assumption and insisted that a kind is only a natural kind relative to a specified enquiry; ie, it's a relation of the form "K is a natural kind for E." (Proposals of this kind have been made by Dupre and Boyd.)
Consider an example like 'race.' There is no essential biological difference between members of different races, and so it may be tempting to say that race is not a natural kind. This flatfooted conclusion that race is not a natural kind only makes sense given the monadic presumption. On the relational conception, all that follows is that race is not a natural kind for biology.
A sociologist trying to understand social stratification and discrimination in the US South (for example) might need to recognize race, at least in some form. If so, then race would be a natural kind for that sociological enquiry.
It's tempting to say that race is not a natural kind because we want to deny the bogus rationale for discrimination. Recognizing race as a natural kind for sociology doesn't undercut that, however, since the sociologist's 'race' category couldn't justify the practices that it is used to explain.
To take a different example, biological kinds will not be natural kinds for particle physics - but they are nevertheless natural kinds for appropriately specified enquiries.
Although Dupre proposed a relativized conception of natural kinds over twenty years ago, the monadic presumption is still alive; eg, Bird and Tobin, in the SEP entry on Natural Kinds, simply presume it.
What I'm wondering is whether you, reader of this blog, consider the monadic presumption to be the default view of natural kinds. How heterodox is the relativized conception? Do you even consider the relativized conception when you think about natural kinds?