Most rear racks are stabilized sideways by having two supports coming up from the rear dropouts on each side. One support comes up verically to the edge of the top platform, while the other goes to the centre at the back of the top platform. When viewed from the rear these supports form rigid triangles. You should try and mount your baskets on a rigid rack like that. Your rack with only 2 parallel vertical supports can sway like a parallelogram.