It's usually those fancy sites with lagging animation and absurdly large text. They don't know server-side rendering and their entire front page is a React component.
As of how many... feels like 1 in 20.
I work on a subscription product that uses React and doesn't show anything if you have no Javascript... Not because there is any blocking but because it fundamentally depends on it.
About one in thirty (ish) - relatively rare, but still too many [1].
I can speak with some confidence as I browse almost exclusively without js. If a site needs it, I just move on [2].
Most sites still render a lot (sometimes revealing more) of their content perfectly without it.
As other HN commentators have noted, there's a strong negative correlation between sites that are js heavy and quality. Very little of value is lost by avoiding them.
[1] Too many because it seems a those that don't work without js also break legally required accessibility standards and are mainly from bigger entities who should behave better.
[2] About the only thing I can't seem to do on HN as a text-only reader is up/down vote other posters. That's also a feature.