@angus, @dbwhite a possible cause of the issue could be if the WordPress site is using Woocommerce. Woocommerce adds a login redirect that can cause issues with DiscourseConnect. Those redirects can be overwritten by either installing and activating GitHub - scossar/wp-discourse-woocommerce-support: Integrates the wp-discourse plugin with WooCommerce, or by adding the code snippets that are given in that plugin’s readme to the site’s theme.
The redirect issue that is being described here seems similar to what I’ve seen with other Woocommerce sites in the past. In those cases, it’s been resolved by installing the WordPress plugin that I linked to.
If this is the cause of the issue, I wonder if we should look into adding Woocommerce support directly to the WP Discourse plugin.