This letter describes a new type of soft robotic grippers with variable stiffness to grasp efficiently a wide variety of objects. The gripper includes two sections, a pneumatic chamber for actuation and a tipping section for adjusting stiffness and shape adaptation. The tipping section consists of Magneto-rheological (MR) fluid, a magnetic source, and a tactile sensor. The MR fluid is responsible for changing the stiffness and it is solidified using the magnetic source which is a combination of magnetic elastomer, an electromagnet, and a permanent magnet. The tactile sensor is embedded within the soft finger to detect contact with the object and to trigger the magnetic source. Five experiments have been conducted to evaluate the gripper's performance, stiffness, and success rate. Results indicate that the proposed soft gripper is an effective design that can ensure robust grasping of a wide variety of objects. Furthermore, the study demonstrates that our design can change stiffness in less than one millisecond while increasing the applied force by approximately 2.5 times. In addition, by matching the fingertip to the shape of the object, the gripper exhibits a high success rate (more than 85%) ensuring reliable and secure grasping when the MR fluid solidifies.