Interactive exploration of the unknown physical properties of objects such as stiffness, mass, center of mass, friction coefficient, and shape is crucial for autonomous robotic systems operating continuously in unstructured environments. Precise identification of these properties is essential to manipulate objects in a stable and controlled way, and is also required to anticipate the outcomes of (prehensile or non-prehensile) manipulation actions such as pushing, pulling, lifting, etc. Our study focuses on autonomously inferring the physical properties of a diverse set of various homogeneous, heterogeneous, and articulated objects utilizing a robotic system equipped with vision and tactile sensors. We propose a novel predictive perception framework for identifying object properties of the diverse objects by leveraging versatile exploratory actions: non-prehensile pushing and prehensile pulling. As part of the framework, we propose a novel active shape perception to seamlessly initiate exploration. Our innovative dual differentiable filtering with Graph Neural Networks learns the object-robot interaction and performs consistent inference of indirectly observable time-invariant object properties. In addition, we formulate a $N$-step information gain approach to actively select the most informative actions for efficient learning and inference. Extensive real-robot experiments with planar objects show that our predictive perception framework results in better performance than the state-of-the-art baseline and demonstrate our framework in three major applications for i) object tracking, ii) goal-driven task, and iii) change in environment detection.