I'm getting the same Captcha loops with Archive, although I had originally blamed my out-of-date browser. What alternative sites are there?
To whitelist, on Firefox: Hamburger menu > settings > privacy and security > DNS over HTTPS > Manage exceptions > Add "archive.is", "archive.ph", and "archive.today"
If you don't want to do that, or it doesn't work, use Firefox's reader mode or the google cache bookmarklet I added below.
Google Cache Bookmarklet:
javascript:void(open("https://webcache.googleusercontent.com/search?q=cache:" + document.location))