We can filter through many categories at a time. I only want my customers to pick one category to filter, rather than multiple ones. Is this possible?

For categories and subcategories, it is not possible unless you modify the source code from checkbox to radio button. However, if you create custom fields, you may choose a Control Type between Radio button, Checkbox and Slider. In your case, you would choose “Radio Button”. This way, on the sidebar, you would only be able to pick one value under that specific fields.