By default, the Web Store will respect the hierarchy settings when displaying and charging taxes online.
This example is working by design:
1. State is Taxable
2. Customer within that state is non taxable
3. Item purchased is taxable
The expected and actual result should be a non taxed value on shopping cart and checkout because it will follow the tax setting on the customer record.
However, there are some instances where the Web Store shows tax amount even when the shopper has been set to non taxable on the customer record.
To solve this,
1. Navigate to Setup> Accounting> Setup Taxes
2. Find the Charge Sales Tax on Store Orders field
3. Select Per Customer Basis
This might have been set to Always. And Per Customer Basis will follow the customer record's tax setting instead of charging the entire online orders taxes.