Apple - macOS windows requiring an explicit click to make active, before UI elements inside can be clicked

The answer, in general, is "no". There are some exceptions/workarounds though, for example:

• You can click through to any control in an unfocused window using Cmd-Click. This will directly operate that control without focusing the window, which might save you a click in your side-by-side browser window scenario. Unfortunately it's up to each application developer to make this work sensibly, and some unfocused applications will still perform any special action assigned to Cmd-Click, rather than treating it as a simple click.
• In Terminal.app, Cmd-Right Click will paste the contents of the primary selection (the last text you highlighted in any terminal window) into the same or another terminal, whether that terminal is focused or not.
• Specifically for X11 applications running under XQuartz.app (which isn't very many these days), you can specify the "focus follow mouse" option so that X11 windows are focused as you mouse over them. (There also used be a hidden focus-follows-mouse option for Terminal.app windows, don't know if it still works in El Capitan or Sierra.)