We study privacy-aware communication over a wiretap channel using end-to-end learning. Alice wants to transmit a source signal to Bob over a binary symmetric channel, while passive eavesdropper Eve tries to infer some sensitive attribute of Alice's source based on its overheard signal. Since we usually do not have access to true distributions, we propose a data-driven approach using variational autoencoder (VAE)-based joint source channel coding (JSCC). We show through simulations with the colored MNIST dataset that our approach provides high reconstruction quality at the receiver while confusing the eavesdropper about the latent sensitive attribute, which consists of the color and thickness of the digits. Finally, we consider a parallel-channel scenario, and show that our approach arranges the information transmission such that the channels with higher noise levels at the eavesdropper carry the sensitive information, while the non-sensitive information is transmitted over more vulnerable channels.