After investigating further, I realized it doesnt have much to do with the plugin itself rather than Cypress itself. So my prod has an SSO subdomain and a subdomain for the app itself. When visiting the login page, you can only see the SSO subdomain under local storage, both in the runner and in Chrome. However, after you log in, the SSO subdomain is removed in Chrome local storage, but persists in the Cypress runner, which causes the tests to set and get local storage items from the wrong subdomain.
Any ideas for a workaround here? I've set the baseUrl to the app's subdomain, but since login needs to take place before accessing that, the ancestorOrigin will still be the SSO's subdomain.