I doubt there is one person in 10,000 that has a clue what the issues are that they are complaining about.
I doubt that very many people would care if the union crumbled and the writers were replaced by non-union writers.
I'm sure there are quite a few people who miss seeing new episodes of their favorite shows, but I highly doubt they care if the writers are union members or about the details of their contracts. They likely simply care that the media companies pay well enough to attract good writers, which in some cases they apparently do, and in a lot of cases they apparently don't.
When I say “support from the public,” I mean those surveyed who know and care about the issue. The general public - that is to say, noncombatants outside Hollywood - rightly have much more important things to worry about. Such as Brittany’s mental health issues.