The gist is, archive.today configured their DNS server to use edns client subnet to determine the visitor's general location to direct them to servers closest to their area for load balancing purpose. Cloudflare DNS however doesn't pass that information for privacy reason. I guess this piss archive.today's dev off because their dns-based load balancing is no longer work effectively for cloudflare DNS users, so they outright block it.
On my network, I send dns requests for only the archive domains to a DNS server that archive likes. Adguards, in this case. Everything else goes to cloudflare. Both adguardhome and unbound can do that.