How to hide tags from wordpress site posts without removing them?

The easiest way to achieve this would be to edit your theme and remove the tags there that include the tags in the template. By doing this they will still exist and be shown in the backend but will not appear on the post (or on any other page that you remove them from).

While it’s possible to directly modify your WordPress theme you should do this only if it is a custom theme that will not be updated by the author as a packaged theme. If this is a standard theme or one that will be updated you should create a child theme where you can make your changes so they won’t be broken or reverted by an update.