I agree that the BBC were extraordinarily inadequate during the Brexit debate—they remain dangerously misinformative now. But, returning to community activity, it's slow, but powerful. If you can change one person's mind over the course of four years, that equates to a vast swing in public opinion.
You must, and I mean this genuinely, have a unique sample pool of reasonable people. People I know well, knew before & still know, at best refuse to talk about it. No, zero, nulla online interactions have resulted in a single backward step in 10yrs.
Online is the wrong place. Try in person. And keep going. Just have normal conversations. Don't explicitly try to convince anyone of anything. Just ask questions, have a laugh, get people to think. Over four years, one of those conversations will bear fruit.
Here’s the thing…I’m a lawyer, I’m trained to ask questions & choose my words carefully - in respect of any dialogue with leave voters, there isn’t any fucking English language that encourages more than them putting their fingers in their ears. You seem uniquely capable.