Login with cache

You have not shared your website URL so I could not look into the issue myself but here is what I have to say.

Generally this plugin will BYPASS cache for the default login pages like /wp-admin/, wp-login.php and so on.

But if you have a custom page for login in your website i.e. https://example.com/log-us-in/ in that case you have to manually bypass cache for that page in the Prevent the following URIs to be cached section. Screenshot: https://i.imgur.com/ayza6Kh.jpeg

Now in your case, you mentioned a popup for login. Now I don’t know if you are using Ajax to login people or using the normal method. Basically wherever you have a login page, you cannot cache that page.

Because when that page is cached and is being served from Cloudflare CDN – then the PHP doesn’t run which is necessary for the login process to happen.

Also on your site if you have a customer-facing login logic, I will highly recommend you to use the Worker Mode instead of the default page rule mode inside the plugin.