As far as I am aware, all previous issues with archive.today and Cloudflare were on account of archive.today taking measures to stop Cloudflare's DNS from correctly resolving their domains, not the other way around.
The current situation is due to Cloudflare flagging archive.today's domains for malicious activity, Cloudflare actually still resolves the domains on their normal 1.1.1.1 DNS, but 1.1.1.2 ("No Malware") now refuses. Exactly why they decided to flag their domains now, over a month after the denial-of-service accusations came out, is unclear, maybe someone here has more information.
Sounds a bit like when "Finland geoblocked archive.today". In all actuality, there was no geoblocking of the site in Finland by any authorities or ISPs, but rather it was the website owner blocking all Finnish IPs after some undisclosed dispute with Finnish border agents. When something bad happens, people seem a bit too willing to give archive.today the benefit of the doubt.
For context, archive.today is angry that Cloudflare won't pass through EDNS - which includes things like your IP address, which archive.today explicitly wants for DNS-based geographical routing. The obvious problem with this is that it would deanonymize all 1.1.1.1 users, at least down to their ISP and probably down to the individual subscriber.
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