Opinion dynamics research uses mathematical modeling and network science to understand how opinions spread and evolve. Rewiring, the process by which individuals modify their social networks, plays a pivotal role in this phenomenon. In this study, we examine the effects of probabilistic rewiring and the presence of zealots using an expressed-private opinion model with bounded confidence. Agents sever links with neighbors whose opinions deviate significantly from their own. Two rewiring scenarios are considered: In the first, agents reconnect with another neighbor to maintain a fixed number of links. In the second scenario, the severed links may not be replaced. Our findings reveal that rewiring reduces pluralistic ignorance and hidden extremism by allowing agents to adjust their social networks and resist extreme opinions. However, the presence of isolated agents amplifies extremism and polarization, highlighting the critical role of social connections in fostering moderate opinions.