We introduce fully stochastic layers in vision transformers, without causing any severe drop in performance. The additional stochasticity boosts the robustness of visual features and strengthens privacy. In this process, linear layers with fully stochastic parameters are used, both during training and inference, to transform the feature activations of each multilayer perceptron. Such stochastic linear operations preserve the topological structure, formed by the set of tokens passing through the shared multilayer perceptron. This operation encourages the learning of the recognition task to rely on the topological structures of the tokens, instead of their values, which in turn offers the desired robustness and privacy of the visual features. In this paper, we use our features for three different applications, namely, adversarial robustness, network calibration, and feature privacy. Our features offer exciting results on those tasks. Furthermore, we showcase an experimental setup for federated and transfer learning, where the vision transformers with stochastic layers are again shown to be well behaved. Our source code will be made publicly available.