Keeping in mind that if the attached box is a commercial streaming device, it will likely spy on you as well: Data collected on me by ROKU
It would be better, privacy-wise, to connect a trustworthy Linux computer and use a privacy-respecting browser to access streams, if possible - a browser with appropriate privacy extensions (NoScript, uBO, Privacy Badger, etc.) installed.
Of course, installing Pi-hole on your home network and loading up some of the well-known public anti-tracker lists can prevent much of the data-slurping, whether from a TV or a streaming box, or a computer. (We all hope.)