Cant sign into any Google iOS app
Download the Google Chrome app on the iPhone and sign in to your Google account in the Chrome app.  Then open the Gmail app (or any other Google app) and you should have an option to slide a switch and be logged in to your account in the Gmail app as well.  if you don't get that option try deleting and re downloading the Gmail app.

Problem seems to be between Safari and the Google login, in my case with two-factor enabled.