Verizon may not listen to your calls, but they do track the IP addresses your phone connects to and what you do on the internet to profile you.

Source: PII data request of my own Verizon account, containing detailed demographic data, intent/interest data, and IP addresses of websites I had visited.

Edit: Anyone interested in doing the same, here's the link: https://www.verizon.com/support/download-and-view-vpd-file/