This is something you see often nowadays, especially on social media. Activists get some controversial policy approved, or censor some already-existing content. Yet if you protest it, you get the "dude why do you care" fence-sitters. They'll tell you that it doesn't matter that much and that both sides are silly anyway. Often these people are in complete support of said policy/censorship, but if you point it out they'll just tell you that those extremists don't represent them (because they're the enlightened "centrists", of course), and you get nowhere.
I feel like this is a big problem. How do you deal with this?
Do not underestimate the number of people driven by idiocy, laziness, comfort, and lack of care. Those are, and always have been, the drivers of the fence sitters. It's a symptom of a successful society, that can insulate such idiots from immediate ramifications of mother nature. These idiots usually go along with the mainstream, regardless of what it is or does, because it's easy, and help facilitate the downfall of successful societies, moving away from what made them successful, and toward collapse, when people move closer to nature, when such idiots will be deservedly killed off for being stupid. This is a much bigger topic, but I'll end it here.
I think people vastly overestimate how little other people are aware of the things inside your own bubble. You could be of the opinion that "Surely everyone knows x, y and z", but you go and ask almost anyone you know and their response is likely "What is x, I've neither heard nor care about y, and z is a thing? Why is z a thing? That's dumb!".
Most people aren't politically engaged- even tangentially. I remember asking a couple of my friends(American) about Kony 2012 a few years ago- which I thought had exploded all over the internet and become a household name. My friends had never heard about Kony or even the "Bring back our girls" campaign with Big Mike(at the time was 1st lady).
It's hard to care about something you are completely unaware of. The left and uniparty are in control of most media, so our biggest hurdle is just getting people to know there is an argument taking place, let alone which side they need to take.