Because the tax status is still determined within your customer's individual customer profile, adjusting their taxation status from customer to customer is as easy as opening their profile and adjusting the setting.
Once you open a customer's account profile, you should see a 'Tax Settings' subsection.
If you click the 'Manage' button found within that settings subsection, you'll be shown this menu:
You can now choose to tick or untick the box that says 'Collect Tax'.
Unticking the box will cause your customer to be tax exempt.
Ticking the box (as shown in the image above) will cause them to be charged any applicable taxes you've set up.
Once you adjust as needed, you can click the 'Save' button, thus updating your customer's taxation preferences.
You can adjust your customer's taxation status as often as needed, and will follow this process to do so each time.
Shopify offers a guide to this process as well, which can be found here.
Note: In order to charge taxes to your customer, you must both set them up to collect taxes, as well as mark your products as 'Charge taxes on this product'. If you've only set up one of these two settings, no taxation charges will be issued.