Well, in my opinion, it can. And so do social movement scholars Gabriel Holland and Jeff Goodwin. Given the history of social theory since the unlamented demise of the USSR, sometimes the basics of a Marxist approach need restating time and again. Their 'The Strange Disappearance of Capitalism from Social Movement Studies' article in the excellent (but ludicrously expensive) Marxism and Social Movements does just this. Here's a segment summing up why Marxian methodology is vital for getting to grips with all kinds of movements.
Capitalist institutions (factories, railroads, banks, and so on) or institutions that capitalists may come to control (such as legislatures, courts and police) are often the source or target of popular grievances, especially (but not only) during times of economic crisis; these institutions, moreover, shape collective identities and solidarities - not just class solidarities - in particular ways; they also distribute power and resources unevenly to different social classes and fractions of classes; they both facilitate and inhibit specific group alliances based on common or divergent interests; class divisions, furthermore, often penetrate and fracture political movements; and ideologies and cultural assumptions linked to capitalism powerfully shape movement strategies and demands. The effects of capitalism on collective action ... are both direct and indirect (that is, mediated by other processes) and are the result of both short- and long-term processes.
Holland and Goodwin, in Barker et al (eds) 2013, p.85Stated this way, it's common sense. For a case study on social movement history that operates with these principles, I recommend this book.