How can Bitcoin solve societal problems caused by capitalism? While trying to explain Bitcoin to a friend, her response was:


  To me this sounds like just an other monetary system which can be
  speculated on while making some people rich and keeping others poor. How
  does it attempt to solve deep rooted problems in our society caused by
  globalisation and capitalism?


She was of course referring to geographic and social inequalities, exploitation of workers, political oppression, depletion of natural resources, etc. 

What are some of the ways decentralised proof-of-work currencies (and their underlying protocols) can work to improve these aspects of our society?
Bitcoin itself, although conceived from an ideological background doesn't have an agenda. It is a tool. It will not solve societal problems by itself, but might help alleviate some issues, by providing competition to current solutions. Especially, wealth distribution in Bitcoin itself isn't better than in other currencies (see e.g. Business Insider on Wealth Distribution in Bitcoin, BitcoinTalk on Distribution of Bitcoin Wealth).

International Remittances

Bitcoin enables its users to send money for minuscule fees around the globe. This could be especially beneficial to foreign workers that want to send remittances to their families in developing countries. 

Currently, they are dependent on expensive services such as Moneygram or Western Union and lose up to 15% of the sent money in fees. Additionally, the recipient needs to go to the next money transmitter shop to pick-up the money. In many instances this is a trip of hours.

The Unbanked

Bitcoin doesn't require its users to have a bank account, as any form of internet access is sufficient to send and receive Bitcoin. Today, there is an enormous number of people without bank accounts. For example there are about 10 million unbanked or underbanked households in the US. In developing countries more than 50% of the populations are unbanked, women more so than men.

Without a bank account, you are either unable to use or significantly disadvantaged regarding a wide-range of services, such as credits, saving, insurance, payment for contracts, and internet commerce. See for example: Guardian on mobile banking for the unbanked. 

Bitcoin could provide an easy access and cheap payment system for many of these services. It could be significantly cheaper than current payment systems such as M-Pesa, and have additional advantages by not being centrally run. 

Censorship

No user can be locked-out of Bitcoin. On the other hand, it is well known for such things to happen in centralized payment systems for various reasons: eBay and Paypal exports Embargo, Paypal blocks donations to Diaspora. This is especially important for protest movements that might be shut-down by their government, think Wikileaks, Occupy Wallstreet, or Social equality movements in repressive states.