>Do you just whitelist every site you come across if it's broken?
Mostly, yes, often temporarily for that session, unless I do not trust a website, then I leave. How I deem what is trustworthy or not is just based on my own browsing experience I guess.
>What's the security advantage here?
You can block scripts, frames, media, webgl... Meaning no ads, no JS... Which helps minimize the more common ways to spread malware, or certain dark patterns, as well as just making browsing certain sites more pleasant without all the annoying stuff around.
>Or do you bail if it requires javascript?
If I don't trust a website, yes.
>What about the proliferation of sites that don't really need javascript, but you need to enable it anyways because the site's security provider needs it to verify you're not a bot?
Not all sites require JS to work, or when they do, they do not require every single JS domain on a website to work. An example of this would be something like many of the popular news sites which try to load sometimes JS from 10 different domains or more and only really require one or none to be usable. Take CNN, I do not need to whitelist it's main domain via NoScript to read articles or navigate, but the moment I whitelist CNN.com, i see a flood of other domains to whitelist which are definitely not needed, like CNN.io, cookielaw.org, optimizely.com, etc...
Take Hacker News. It's viable without JS, I can read, navigate and comment, but if I want to use the search function, I need to whitelist algolia.com (which powers the search) or else I just see "This page will only work with JavaScript enabled". The search function not working is the most common issue you'll find if you block all JS by default.