"Contemporary folk" and "traditional folk" worked well enough for decades and I don't see the reason to change them now; if it ain't broken and all that. Definitions are too limiting, and do not allow the "thing defined" to evolve. They are also unnecessary at best and can be abused at worst. No, rather than defining folk music of whatever flavour, I prefer to simply describe it periphrastically, based on the impact it has, not on the instruments or the chords or modes it uses.

As for the relationship between folk and the class system, that is a 20th century forcibly enforced connection as far as I am aware, and has no real meaning. Else you wouldn't get the miners' songs next to the Babes in the Wood, next to the hunting songs, next to the Banks of the Nile, all in one genre. Yes, some British folk songs specifically have class importance, but others don't; and other countries' folk songs are (understandably) totally oblivious to the class system.

What is important for all folk songs and music is that they should have relevance to the period in which (note: not "about which") they were written, social relevance in particular. That is why in a folk song lyrics are important, whereas in a pop song they are incidental.

And of course, folk songs/music should be accessible and easily replicated by ordinary people (to whatever standard of excellence is immaterial), so they would have sparse arrangements, even the contemporary ones. That is why "Bohemian Rhapsody" could never be a folk song - too elaborate, even though it caught people's imagination - while Gerry Rafferty was writing effectively contemporary folk hits in the same period.

This insistence on defining "folk" seems to me to be a peculiarly British thing. I certainly haven't come across it in other countries' folk music, including my own home country. There, people don't bother to define "folk" (Laiko, i.e. "of the people") song. When a new one comes across, they just recognise it instantly for what it is, even if it employs totally contemporary arrangements and instrumentation. And so folk grows, and adapts, and adopts, and evolves, and assimilates, and retains its relevance. And still, people will recognise a traditional song or tune for what it is, mostly because of the time-displaced relevance, even if given a contemporary treatment. And yes, there are people who prefer the traditional folk over contemporary, or vice versa, and nobody tries to put down the other.