According to the baby food website I use, the could a mild to highly allergenic food. Although, I know some ladies here have given them with no problem.
I rarely eat blackberries, do they fall apart like raspberries do or are they firmer like blueberries? I might cut them into halves or quarters if they don't fall apart easily, but otherwise I wouldn't have any qualms about feeding them to LO. Be on the lookout for black poop though!