In recent years, recommender systems are crucially important for the delivery of personalized services that satisfy users' preferences. With personalized recommendation services, users can enjoy a variety of recommendations such as movies, books, ads, restaurants, and more. Despite the great benefits, personalized recommendations typically require the collection of personal data for user modelling and analysis, which can make users susceptible to attribute inference attacks. Specifically, the vulnerability of existing centralized recommenders under attribute inference attacks leaves malicious attackers a backdoor to infer users' private attributes, as the systems remember information of their training data (i.e., interaction data and side information). An emerging practice is to implement recommender systems in the federated setting, which enables all user devices to collaboratively learn a shared global recommender while keeping all the training data on device. However, the privacy issues in federated recommender systems have been rarely explored. In this paper, we first design a novel attribute inference attacker to perform a comprehensive privacy analysis of the state-of-the-art federated recommender models. The experimental results show that the vulnerability of each model component against attribute inference attack is varied, highlighting the need for new defense approaches. Therefore, we propose a novel adaptive privacy-preserving approach to protect users' sensitive data in the presence of attribute inference attacks and meanwhile maximize the recommendation accuracy. Extensive experimental results on two real-world datasets validate the superior performance of our model on both recommendation effectiveness and resistance to inference attacks.