the opposite is the case. from your link: "Archive.is’s owner is intentionally blocking 1.1.1.1 users"
Cloudflare blocks the extension to DNS that allows that. If you don't care, you can set your DNS to bypass Cloudflare for those domains only.
That being said, by "Cloudflare has issues with archive.is" I very literally meant that they have issues with the DNS records served to them by Archive.is. (i.e. They do not support EDNS.)