Integrated sensing and communication (ISAC) has been identified as a promising technology for the sixth generation (6G) of communication networks. Target privacy in ISAC is essential to ensure that only legitimate sensors can detect the target while keeping it hidden from malicious ones. In this paper, we consider a downlink reconfigurable intelligent surface (RIS)-assisted ISAC system capable of protecting a sensing region against an adversarial detector. The RIS consists of both reflecting and sensing elements, adaptively changing the element assignment based on system needs. To achieve this, we minimize the maximum sensing signal-to-interference-plus-noise-ratio (SINR) at the adversarial detector within sample points in the sensing region, by optimizing the transmit beamformer at the base station, the RIS phase shift matrix, the received beamformer at the RIS, and the division between reflecting and absorptive elements at the RIS, where the latter function as sensing elements. At the same time, the system is designed to maintain a minimum sensing SINR at each monitored location, as well as minimum communication SINR for each user. To solve this challenging optimization problem, we develop an alternating optimization approach combined with a successive convex approximation based method tailored for each subproblem. Our results show that the proposed approach achieves a 25 dB reduction in the maximum sensing SINR at the adversarial detector compared to scenarios without sensing area protection. Also, the optimal RIS element assignment can further improve sensing protection by 3 dB over RISs with fixed element configuration.