We may even need something stronger than docker. There are various project to use virtualization technology to sandbox a browser session at the hardware level. My guess is that ultimately this is the future of web browser.

One commercially supported Windows [browser] application virtualization (-ish, pretty much Docker-grade security for end users) option, $35 for personal use: https://www.sandboxie.com

Most similar tools are marketed as antivirus products, and are only available via enterprise licensing and/or SaaS reporting. An example of a hardware virtualization based option: https://www.bromium.com/platform/our-technology.html

Or firejail