A business is more than just the source code. The source for Reddit, for example, is OSS. So anybody should be able to put Reddit out of business in a few days, right? But yet... nobody has. Hmmm....
So yeah, you can distribute source code and still make money. Lots of companies do it. Red Hat, SugarCRM, Alfresco, etc.
In some ways it's probably even easier for an online service to both be OSS and be successful, exactly because it takes all the other "stuff" (hosting, devops, marketing, network effects, etc.) to be successful. And, in fact, there are OSS replacements for things like Facebook and Twitter. The problem is, very few people use them for whatever reason (probably mostly network effects).
So at least in regards to the Facebooks, Twitters, etc. of the world, the first question you'd have to answer, is how to get people to switch to your service, whether it's free software or otherwise.
That depends on your business and your business model. Some business models only work with at least partially closed source software while some profit from open source licensing (when applying a dual licensing model for instance).
Stallman is an extremist: To him every piece of software has to be free (as in speech) and if it isn't it's evil. He is an activist. So, it's fine for him to have that kind of worldview. The real world and pragmatic solutions often aren't simply black or white, though.
"Business models for open-source software" https://en.wikipedia.org/wiki/Business_models_for_open-sourc...
...
- https://github.com/GoogleCloudPlatform
- https://github.com/kubernetes/kubernetes (Apache 2.0)
- https://github.com/apple (Swift is Apache 2.0)
- https://github.com/microsoft
- https://github.com/twitter/innovators-patent-agreement
...
- "GNU Social" (GNU AGPL v3) https://en.wikipedia.org/wiki/GNU_social
... http://choosealicense.com/appendix/ has a table for comparison of open source software licenses.
http://tinyurl.com/p6mka3k describes Open Source Governance in a chart with two axes (Cathedral / Bazaar , Benevolent Dictator / Formal Meritocracy) ... as distinct from https://en.wikipedia.org/wiki/Open-source_governance , which is the application of open source software principles to government. USDS Playbook advises "Default to open" https://playbook.cio.gov/#play13
Anarchy / Budgeting: https://github.com/WhiteHouse/budgetdata
Easiest (lowest risk) method AFAICT is consulting. Make a webpage, do some SEO & a few keynote talks at big conferences. Once the consulting is paying well, quit your (presumably proprietary) job & only accept projects that involve free software. See e.g. https://blogs.gnome.org/bolsh/2009/02/01/free-software-consu..., there are tons of wordpress shops for example.
Another method is to get skilled in another profession, e.g. law degree, accountant, chiropractor, etc., work in that for a while, build up some custom OSS software to use in that work, promote it & get a userbase, then quit the main job and sell software support / premium addons.
Final method is crowdfunding, for example see https://en.wikipedia.org/wiki/Diaspora_(social_network) as a free software version of Twitter/Facebook, although I think crowdfunding has gotten harder since then so now you need an MVP or something to succeed. It's great for consumer software, particularly for moving codebases from beta-quality to production-ready.