There's some issue with DNS over HTTPS, so you have to whitelist their sites in your settings, or turn off DNS over HTTPS (which I don't recommend).
To whitelist, on Firefox: Hamburger menu > settings > privacy and security > DNS over HTTPS > Manage exceptions > Add "archive.is", "archive.ph", and "archive.today"
In my case I added override rules in my opnsense router so that archive.is .ph .today .md are all resolved by a different nameserver.
Disabling DOH can appear to fix it only in the happenstance case that the fallback plain dns doesn't end up using cloudflare, or doesn't use it first.
https://mullvad.net/en/help/dns-over-https-and-dns-over-tls/
No issues with any archive-sites.
Aside from not being censored at all, thereby enabling visiting sites which are blocked at DNS-level in some locations, there are several options for adblocking at DNS-level, too. Often eliminating the need for a Proxy or VPN to get access, with optional Adblock as a service.
For free.
It's nice.
There is no special reason not to use cloudflare dns in general though.
The problem is only between cloudflare and archive.is (and it's aliases) and it's hard to say if either side is wrong, except for the fact that either or both of them could figure out some special exception where they recognize each other's traffic if they cared to. Cloudflare are not censoring archive.is for example, and are not doing anything wrong.
Then I tried Mullvad-DNS, the speed was still there, the 'lawful' censoring was gone, the problems with archive-sites ceased to exist, and somewhat configurable adblocking-as-a-service.
It's a seamless 'plugin'-solution, not degrading anything.
Triple-A!