Hi, I'm a new forum's member.
Looks like the presence of the blue border around tabs depends on Gtk theme, used for Applications in Gnome 3.
For example, I use PRO-Dark-GTK theme, and there is no blue border in Chrome, with Appearance set to GTK+.
There is no blue border with the set of MATE-Colors and many other Gtk themes either. The border do appear, when the default Plata themes are used for Gnome's Applicattions.