Create a new Tax Rule: Magento > Stores >Tax Rules 

Click "Add New Tax Rule"

Under "Additional Settings" click Add New Tax Class 

Create a Tax Class called "Tax Exempt" and click the check mark.

Create a new Tax Rate called "Exempt"

Create a new Customer Group by going to Stores> Customer Groups and selecting "Add New Customer Group".

Click Save.

To assign the newly created group to customers navigate to Customers > All Customers and check the boxes for the customers you'd like to assign.

In the top left, select Actions and choose Assign a customer group.

Select Tax Exempt.

Now the customer(s) you selected should be assigned to the tax exempt group.

Once this setup has been completed run a test transaction for this customer to ensure that they are NOT charged tax when shipping to a state that you would normally be charging tax for.