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Paul Graham says it's more like 90 or 95%.

"You could probably expand that 80% to 90% or even 95%. The extremists seem like they're more numerous than they are, because they talk so much and so loudly, but they're really a tiny minority." https://twitter.com/paulg/status/1598720168737345539

I remember some stat that the loudest voices are the 8% on either end of the political spectrum. I couldn't find where I heard that, but Pew has some data that mirrors that.

I think that 20% is coming from this:

"The overall share of Americans who express consistently conservative or consistently liberal opinions has doubled over the past two decades from 10% to 21%"[1]

[1] https://www.pewresearch.org/politics/2014/06/12/political-po...

It's unclear what "serving the center 80% means" but I doubt it means banning the remaining 20%.