The main way I've found to trigger this is by searching games via a tag, then changing the sorting order, so that the URL looks like, e.g. https://itch.io/games/newest/tag-singleplayer. In this example, I can search by newest, or I can search by tag: singleplayer, but if I do both I get stuck in a Cloudflare verification loop. This has been going on for months. At first I thought this was on my end, until I found a forum page (that I can't find now) that said that this can happen when cloudflare has a bad url pointer, where the urls don't exactly match or something.
Not using any vpns.