If you want to know which browsers do or do not respect your privacy, check out the site below. They put a wide variety of desktop and mobile browsers through a battery of tracking and other privacy tests. Click on each test for more details.
I post this site every year or so, which is why I wasn't surprised about the recent news regarding Chrome "incognito" mode. It's unfortunate that it took so long to be widely reported.
On my phone (Android) I use Chromite, a privacy-hardened fork of Chromium. It's not on the above site, but it's predecessor Bromite was and had received top marks.
@voltronic firefox focus is a good android browser focuses on privacy and security over anything else
no frills when it comes to settings either
a good browser to set as your default one for opening URLs via Social media it'll wipe everything after you use it