This Captcha issue occurs with non-cloudflare resolvers as well, although with great inconsistency. It depends on the resolver and the user's location when they query. Results can change hours later.
I also used the command `sudo dscacheutil -flushcache; sudo killall -HUP mDNSResponder` on Terminal (double-check this command before using) to flush the DNS cache, so the change would immediately take effect with the archive websites.
Getting Captcha'd happens with non-cloudflare resolvers as well, tho not universally nor consistently.
I forced all of Archive domains to query against Quad9 and started getting unskipable Captchas months ago - when I was local(US).
When I placeshifted to overseas, Quad9 resolved to different IPs and those were usable.
Cloudflare doesn't support a DNS extension that allows this (eDNS maybe?) and so it fails.
Any inference that the Captcha issue is limited to CloudFlare users is incorrect.
Their captcha page is odd, styled to look like Cloudflare's captcha gate but uses reCAPTCHA which Cloudflare publicly spoke about switching from.
Code of the page also seems to include a strange XmlHttpRequest to some blog site with randomized query string (see end of https://pastebin.com/W21Au8RK), along with some fingerprint library (though commented out)
That blog site loads very slow for me if I go there manually - maybe some kind of DoS being directed to it?
Seen this same faux-cloudflare page used on btdig.com too, with the same strange XmlHttpRequest & fingerprint code, pretty weird.