Wouldn’t the time travelers try to fit in so they do not disturb the culture?

• Use a privacy conscious browser like Mulvad or Tor browser.
• Use a VPN or Tor.
• do not be logged in to google/Facebook account while browsing other sites.
• Use an add- and tracker- blocker like ublock.

Many routers have an option to login to a VPN. Then all traffic that goes over that router to the internet goes over the VPN. Theoretically something like that should also be possible with a Linux server if the server is local. With this setup you shouldn’t need to configure the VPN on your local devices.