That kind of browser sounds useful, more so particulary on mobile devices Chrome/Android/Google is incredibly 'sticky' in that it tries to quietly log you in all the damn time.
I then proceed onto the settings app, into 'accounts'. There, I tap 'Google' and lo and behold: App-data, Calendar, Contacts, Google Fit Data and People details are all ticked to sync.
I turn them off.
Then I open the default browser. It logs me into Google, by default. I have to explicitly tell it not to.
Google really really wants users to be logged in. That is my experience anyway.