It's still pretty tied to Google; the routine reminders to "sign in with your Google account!" are one aspect of that.
That said, it's still pretty open as well, and being FOSS, it's certainly doable for there to be a fork (if there isn't one already) that strips out everything Google-related.
No, I'm thinking of Chromium. I use Chromium rather regularly. Last I checked, the various prompts for me to log in with my Google account when starting up a fresh install of Chromium aren't my hallucinations.
That said, it's still pretty open as well, and being FOSS, it's certainly doable for there to be a fork (if there isn't one already) that strips out everything Google-related.