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.