In this paper, we propose a privacy-preserving image classification method that uses encrypted images and an isotropic network such as the vision transformer. The proposed method allows us not only to apply images without visual information to deep neural networks (DNNs) for both training and testing but also to maintain a high classification accuracy. In addition, compressible encrypted images, called encryption-then-compression (EtC) images, can be used for both training and testing without any adaptation network. Previously, to classify EtC images, an adaptation network was required before a classification network, so methods with an adaptation network have been only tested on small images. To the best of our knowledge, previous privacypreserving image classification methods have never considered image compressibility and patch embedding-based isotropic networks. In an experiment, the proposed privacy-preserving image classification was demonstrated to outperform state-ofthe-art methods even when EtC images were used in terms of classification accuracy and robustness against various attacks under the use of two isotropic networks: vision transformer and ConvMixer.