Hi webfactoria,
Even when active, Hide My Site doesn’t make any changes to htaccess or reroute any URLs. It also does not make any changes to the code in any of your other WordPress files.
When Hide My Site is deactivated, it will no longer run on your site, effective immediately.
However, some sites have a caching system whereby old versions of the site continue to be shown to site visitors. This means that even though you have deactivated/deleted a plugin from your site, the cached (older) version of your page might still be shown to your visitors – and that older version of the page can be from a time when you still had the plugin active on your site.
It could be that your site is partially trying to run an older, cached version of your site – from when Hide My Site used to be active. Since Hide My Site is in fact no longer active on your site, this could be why your site is breaking since the plugin is in reality no longer active and available to be used.
Many times users think they have cleared all the cache, however in the end it turns out there is some cached version of their page that is being served to site visitors. Often times cached pages are served automatically via your web host, and many users are not aware of the fact that their web host does this.
If you are using wpengine (or a different host that auto-caches) try reaching out and ask if they can clear your cache for you. If you are not sure if your web host auto-caches, try sending your webhost a message and ask if they use an auto-caching feature on your site.
Hopefully this will be able to help clear up the issue for you. If not, feel free to email me direct via justin[at]clevelandwebdeveloper[dot]com and I can try and look more into this for you directly.
Best,
Justin