How to make https links available to anonymous when new article is published?
Assuming both secure and non-secure websites are in fact the same Drupal instance, there are a few possibilities which may cause the issue you are experiencing:


Web server; configuration differences in secure non-secure sites.
Compare both website settings. Only difference should be SSL specific settings, rest should be same or inheriting settings from other's. if necessary, refer to web server's official documentation.
Web server; misconfiguration in redirect rules
From your comments it's clear that both websites are actually available. Still there could be redirect rules needs correcting.  
HTTP or HTTPS version of the site has an external caching system
Check if there is caching system or proxy enabled for either of the sites. i.e. Varnish, Redis, CloudFlare.


Please provide some more details about the webserver (Apache, nginx, IIS, etc), and currently installed caching and performance related modules.

Also, you can consider serving the site only on HTTPS, to avoid penalties from search engines for duplicate content.