My name is Lilith, I'm on the Social Care team at Shopify.
It sounds like you might be talking about the filtering options on the collections pages. Please let me know if this is not the case.
With Product Tags, it's a great idea to have these available for products on the back end to help you organize your inventory or automated collections easily. Depending on the theme that you have on your store at the moment you may also find that these tags show up on the filtering dropdown menus in collection pages as shown in my screenshot below:
If you have a theme that has this filtering dropdown, your tags will show up there. In order to remove this, you can open up your theme and uncheck the tag filtering option. For example, if Debut is the published theme, you'll want to head over to Online Store > Themes and click on the purple Customize button for the published theme. Once you're there you can follow the instructions below:
Select Collection pages from the theme settings editor header.
Click on the Collection pages section.
Uncheck the Enable tag filtering box.
Once you do those 3 steps you can save your changes and your customers will no longer see the filtering by tags dropdown.
Let me know if that helped! I'm happy to answer any questions you think of as you work on your business.