Sounds like containers and potentially adblocking and js blocking prevent this. For my part, I use linked in on my "god dammnit I hate corporate websites so much" browser which is used only for medical bill pay and amazon / wal mart purchases and then monthly bills. Could LinkedIn get something from me there? Potentially, but they're also not really following me around the web. I think given this I'll go install a 3rd browser for linkedin only, or maybe finally just delete my account. It never got me a job and it's a cesspool.

You can use Firefox with different profiles and configure it to launch particular profile directly, without launching default profile and using about:profiles.

Firefox with a non-default profile can be created like that:

  ./firefox -CreateProfile "profile-name /home/user/.mozilla/firefox/profile-dir/"
  # For linkedin that would be:
  ./firefox -CreateProfile "linkedin /home/user/.mozilla/firefox/linkedin/"

  ./firefox -profile "/home/user/.mozilla/firefox/profile-dir/"
  # For linkedin that would be:
  ./firefox -profile "/home/user/.mozilla/firefox/linkedin/"

    - create a copy of it, say, /usr/bin/firefox-linkedin
    - adjust the relevant line, adding the -profile argument

Of course, "./firefox" from examples above should be replaced with the actual path to executable. For default installation of Firefox the path would be in /usr/bin/firefox script.

So, you can have a separate profiles for something sensitive/invasive (linkedin, shops, etc.) and then you can have a separate profile for everything else.

And each profile can have its own set of extensions.