How did people make their own music before that - 'traditionally'?

The short answer to your question GUEST,jag is - Yes that is exactly how they did it, with regard to Gaelic working songs, they normally had no accompaniment, they had no written music, they were normally made up and sung by women and they were passed on by mouth.

the folk clubs were set up so we could make our own music rather than pay someone to do it for us

That was certainly the case back when "Skiffle" broke away from its Jazz background, and it is the case in my area now where folk clubs book about twelve Guest performers each year. The folk club regulars always turn up to sing and play at the "session" nights but rarely if ever turn up to hear the Guest artists where the clubs get a completely different audience. Unfortunately you never know what you might hear at the "session" nights.