attribute editor/ shapes/ drawing overrides / display type/ reference
I had the same problem today, trying to get rid of the dashed lines for sotf edges (they drive me mad...).
While trying about every option in the attribute editor I went to shapes/ drawing overrides / display type and dumbly checked "reference". Object was unselectable. So select it via the outliner go back to drawing overrides / display type and check "normal" and your object is selectable again.