Philosophers typically seem to prefer unity of doctrine over unity of method. This is particularly evident within philosophical subdisciplines. In metaethics, for example, mixed views such as "expressivism is true for social group X/domain P of moral discourse, error theory for social group Y/domain Q." seem to be relatively unpopular.

But the same phenomenon also seems to hold across subdisciplines: Antirealism/Naturalism about ethics often goes hand in hand with Illusionism/Reductionism about consciousness, and the corresponding views in other fields of philosophy. Jacy Reese Anthis,  Lance Bush, and Eliezer Yudkowski all seem to be antirealists about ethics & illusionists about consciousness.

Unity of method on the other hand seems to be somewhat rare among philosophers, perhaps because many philosophers don’t have a sufficiently clear method (other than “evaluating arguments”) that they could apply across problems/fields.

I think this is problematic and it is often better to have a systematic method that one can apply to many problems, even if it leads to different results in different cases. 

Example: I find conceivability arguments to be a powerful tool to extract the content of concepts & it can be applied to many philosophical problems. But it (arguably) leads to very heterogeneous results: compatibilism about free will is true for some people, incompatibilism for others. Reductionism is true for most things, but not consciousness (either Russellian monism or Illusionism is true for consciousness). Expressivism about ethics is true for many people, but for some either error theory or non-naturalism is true. Etc.