Is there a way to hide cell borders in tables that you create?

To remove borders from table cells you just need to edit the style of your current theme.

To do that, go to the Customization > Manage Templates.
If you already use a custom theme, apply changes to it. Otherwise you need to create a new theme by clicking on the green plus button, apply changes to it and then go to the Customization > Styling and Front-end Settings and enable the new theme.

What changes should be done.
Open the CSS > CSS template. Find the following text and delete or comment it out:

Click the "Apply" button, and this fix will be applied to your current theme in both front-end and WYSIWYG editor.