They have the right to do so. I do not have a problem with them being responsible for the security of people in their stores, then.
They have very aggressively banned the carry of weapons in their stores.
Everyone has the right not to shop their, and to complain to management.
I’m going to find out, in the case of half price books, where their main HQ is, and write them about this.
Plus any other stores I run into that has ‘no carry at all’ signs.