A good amount of these websites are proxied by Cloudflare, so you're connecting to CF and CF connects to the website.

And many websites use CF, so if you were to block a CF IP, you'd block a whole bunch of websites.

In that case, what makes Cloudflare immune to court ordered blocks?

You've identified exactly the problem. They'd be blocking thousands of unrelated innocent websites. Also, changing your IP address is really easy.

That’s something cloudflare doesn’t want either. They wouldn’t even need to do it, just threatening to would have a financial impact on cf.

More likely the opposite. A site which is legal in the US or elsewhere but not in the EU would then have fewer options for finding a convenient host, even though it's perfectly legal in the country where it actually operates, because the EU would be exerting extrajurisdictional pressure on hosts by blocking all of their other customers. Those customers would then prefer a host large enough to resist that pressure, which is Cloudflare, because a country that tried to block them would break the internet in their country. And then Cloudflare would improve their reputation among customers by resisting an attempt to DoS a site which is legal where it operates.

Meanwhile it would do nothing to put the site offline regardless because there are more hosting companies than there are atoms in the universe and many of them serve primarily local clientele and wouldn't really care if they got blocked in a country where their customers aren't. They'd have to be blocking the majority of the total IPv4 address space before the site ran out of somewhere to move.