As explained at T226545#5291967, the "Login with Discourse" link at the https://space.wmflabs.org sidebar might have something to do with the signup loop problem.

Let's remove it for now. Only contributors to the blog need that link, which can be placed i.e. in the footer, or in the page explaining how to contribute a blog post.

Instead, and also for now, we can add to the sidebar a link "Join Wikimedia Space" pointing to https://discuss-space.wmflabs.org/t/how-to-join-wikimedia-space/113

All these are interim solutions while waiting for T215052: Add MediaWiki login support to Discourse.