You are right, you can’t get away from Google, even if you stop using Google Search.

Firefox comes with a Google search bar by default. I removed it and replaced it with a Yahoo search bar. I also removed any reference to Google in Firefox and Thunderbird.

After doing that, I found that Avast Network connections is still allowing Google to establish a connection with Firefox and Thunderbird.

What is even worse is that Avast uses Google for some unknown purpose, and allows Google to establish a constant connection through AvastUI.exe, and if you disable this, your connection to the Internet is gone.