Can a store make a veteran choose between their discount and the use of tax exemption?

Stores don’t have to give you either. Your state does tax exemption for 100% for state owned businesses, not private institutions. It’s up to them whether or not they honor one or both.

This question makes you sound like an entitled veteran.

I wouldn't rock the boat. I accept discounts as a courtesy from the participating business. They don't really have to do that much for you. In Tennessee the 10% most businesses give Veterans basically covers the tax. Be thankful for any discounts!

So a store is wanting to honor one offer but not both simultaneously? Stores generally have the discretion of approving/denying discounts but considering you are talking about State Law you may need to reference someone who works closely with the State agency that manages this program. Or you could find a Vteran Advocate from the county or State that could answer your question.