Can Western theories of IR be relevant in understanding non-Western actions?

I think that's a fantastic question, but it's one that is difficult to answer without considering the level of analysis problem. Not all IR theories try to explain experiences of different sets of people or societies, per se.

If you consider IR theory to be essentially abstract theories with states (countries) as actors, then I think it is easier to apply "Western" theories to think about issues surrounding allocation of resources, power, etc. And, much like how economics might apply macroeconomic theory across the board, I think this is fine as long as you are clear on the boundary conditions (being clear about what the theory tries to explain for whom -- and what the theory cannot explain).

However, if you want to consider sociocultural and other differences across societies (which is what I think you are thinking), then major schools of thought in IR, as they exist in the US at least, can seem quite limited. Constructivist theories seem to open up to these types of discussion the most, but there is a lot more work to be done in this area. (Some IR theorists might argue that this is type of work is more for sociologists and other types of social scientists, though.)

It's worth noting that certain frameworks (e.g., theories about bureaucratic politics) also allow some flexibility for studying the content and social influences among relevant actors. But, applying them systematically can be quite difficult, so this could be part of the reason why IR theory tends to go for more generalizeable patterns at higher levels of analysis.