Chromium is pretty safe to use. There are also builds of "de-googled Chromium" available.

Vivaldi, though it's source available rather than fully open source. It's mostly the frontend JavaScript (I think?) code which is proprietary.

Apparently, if you know enough to understand it, you can technically work out what all the proprietary code is and does because it's all fairly simple stuff and separate from the Chromium base (which they make available on their site), although distributing it would be against their ToS (I guess it's technically reverse engineering, which is also against their ToS).

It's been a very long time and I can't actually confirm that for the current release, but it was at least true a few years ago when someone who knew far more about programming than me mentioned it on their forums. I think some people took a look at it and found some basic theming stuff, but nothing nefarious.

They have a fairly solid privacy policy last I checked. They also have no intention of sticking with Google's v3 plans.

The only thing I don't like is they run a daily user count check by pinging their servers. They've made it so that there are no IDs, anonymized or otherwise, but it's still a bit of a black mark on an otherwise decent piece of software.

Firefox supports them