I live in Maryland, is it illegal to shop at this walmart in order to avoid paying tax?

You can go buy whatever you want but do not take it to another state and resell it for more money

Shop ALL you want. Welcome to Delaware.

Unless you are explicitly making numerous large purchases, I believe you should be fine. Alternatively, if you buy something in a Maryland Walmart, paying tax, take said item to a Delaware Walmart to return the item, and attempt to repurchase the item (being in a Delaware Walmart) to repurchase it without paying tax, that would be frowned upon.

I believe you can shop anyware you want.