Why is tax being collected for a customer that is set up as exempt in ECM?

There are several reasons why this can happen:

If you're using AvaTax for tax calculation, keep in mind that AvaTax has fewer exempt reasons than ECM. It may be the case that you’re using an ECM exempt reason that isn't supported in AvaTax. Be sure that you’re using only AvaTax-supported exempt reasons.
If you're using AvaTax for tax calculation, this can be due to an error in the customerCode. When creating a transaction for an exempt customer, the customerCode must exactly match the customer ID of the certificate that was created in ECM. If these don’t exactly match, then the transaction will be taxable.
Not all exempt reasons are fully non-taxable in all jurisdictions. For example, industrial-manufacturer has a reduced rate taxability at CA.