I think the question should be "what ways could free software play a role in saving the world?".. Which in that case it would be when Elon Musk brings about world-wide free internet, and summons the AI demons.. Then we will all be connected to a central SaaS based network controlled by the NWO backed corporate overlords. And it's only when a few dissidents decide to rebel by using free software to set up decentralized p2p servers, will we see the profit margine revenues of the Google Gods plummet.. Just my two cents, #The_Apocalypse_Is_Coming...

A thought:

I discovered Linux only in 2011/12.
But long before that I was always interested in open structures, micropolitics, and ultimately found places that practice "social utopia". It's amazing to see hundreds, sometimes even thousands of people living in a different society. With all the Good and the Ugly that brings about.
I see many structural similarities with what I later found in the Linux world as well - like I often said: the best thing about Linux, the thing that really blows me away, is that it's a global community effort (and one that works very well I might add).

We are forerunners, and I hope we continue being that.
Every such movement can become popular and will face the challenges of not being a niche anymore, and maybe losing its avantgarde status - but hopefully not its openness. I currently experience this both in Linux and in that other movement. We will see what happens.