Switching to Cloudflare DNS solves archive.today problems? That's strange. archive.today is known for having problems with Cloudflare DNS[1]. Switching to Google DNS should solve it. (This isn't because of a bug in Cloudflare DNS, but rather that archive.today dislikes that Cloudflare DNS doesn't support EDNS.)
Disclosure: I work at Google, but not on the DNS team.
Archive blocks VPNs. If you're on one, that could be why.
I've also found that archive.ph is significantly less accessible than archive.is despite hosting the same content. Pausing my VPN for a few minutes and then changing the .ph to .is fixed a similar captcha loop for me, though I still did need to solve a captcha for it.
are you using a VPN? that happens often to me. might be a combo of that and ublock origin. I'm guessing archive gets a ton of attacks from VPN so they probably just have rules to captcha any VPN address. I have a local proxy on rpi setup and then a container in firefox that lets me use that to quickly swap to a proxy that uses my real IP. very handy for shit like this.
The guardian does have a semi-paywall in that you can either share your personal data with them or pay. Which in my opinion is a breach of the GDPR but apparently the UK ICO has said it’s fine. Yet another toothless/useless organisation